CAR_simulation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4b8c0acc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# general libraries\n",
    "import time\n",
    "import math\n",
    "import numpy as np\n",
    "from shapely import geometry\n",
    "from shapely.geometry import Polygon\n",
    "import matplotlib.pyplot as plt\n",
    "import pickle\n",
    "\n",
    "# JAX\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "from jax import random, lax, jit, ops\n",
    "from jax.experimental import stax\n",
    "\n",
    "\n",
    "# Numpyro\n",
    "import numpyro\n",
    "from numpyro.infer import SVI, MCMC, NUTS, init_to_median, Predictive, RenyiELBO\n",
    "import numpyro.distributions as dist\n",
    "from numpyro.diagnostics import hpdi\n",
    "from numpyro import optim\n",
    "\n",
    "#plt.style.use('bmh')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "585f6e9e",
   "metadata": {},
   "source": [
    "## Helper functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ad3b5365",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_samps(draws, columns=4, rows=3, figsize = (19,12), ttl=\"CAR priors\"):\n",
    "    fig, axs = plt.subplots(rows, columns, figsize=figsize)\n",
    "    _min, _max = np.amin(draws[0:columns*rows]), np.amax(draws[0:columns*rows])\n",
    "    for r in range(rows):\n",
    "        for c in range(columns):\n",
    "            im = axs[r, c].imshow(draws[r*columns + c].reshape(ny, nx), \n",
    "                                  cmap='viridis', interpolation='none', #extent=[0,1,0,1], \n",
    "                                  origin='lower')\n",
    "                                  #,vmin=_min, vmax=_max)\n",
    "            axs[r, c].set_title(\"draw \"+str(r*columns + c))  \n",
    "            fig.colorbar(im, ax=axs[r, c])\n",
    "    fig.suptitle(ttl, fontsize=16)\n",
    "    plt.show()\n",
    "    \n",
    "def plot_truth_estimate(y_true, mean_post_pred_vae, ttl1=\"Ground truth\", ttl2=\"CAR estimate\"):\n",
    "    fig, axs = plt.subplots(1, 2, figsize=(12, 4))\n",
    "    _min, _max = np.amin([y_true, mean_post_pred_vae]), np.amax([y_true, mean_post_pred_vae])\n",
    "\n",
    "    im = axs[0].imshow(y_true.reshape(ny, nx), \n",
    "                       cmap='viridis', \n",
    "                       interpolation='none', \n",
    "                       origin='lower',\n",
    "                       vmin=_min, vmax=_max)\n",
    "    fig.colorbar(im, ax=axs[0])\n",
    "    axs[0].set_title(ttl1)  \n",
    "\n",
    "    im = axs[1].imshow(mean_post_pred_vae.reshape(ny, nx), \n",
    "                       cmap='viridis', \n",
    "                       interpolation='none', \n",
    "                       origin='lower',\n",
    "                       vmin=_min, vmax=_max)\n",
    "\n",
    "    fig.colorbar(im, ax=axs[1])\n",
    "    axs[1].set_title(ttl2) \n",
    "    \n",
    "def plot_truth_car_vae(y_true, mean_post_pred_car, mean_post_pred_vae, \n",
    "                       ttl1=\"Ground truth\", ttl2=\"CAR estimate\", ttl3=\"VAE estimate\"):\n",
    "    fig, axs = plt.subplots(1, 3, figsize=(18, 4))\n",
    "    _min = np.amin([y_true, mean_post_pred_car, mean_post_pred_vae])\n",
    "    _max = np.amax([y_true, mean_post_pred_car, mean_post_pred_vae])\n",
    "\n",
    "    im = axs[0].imshow(y_true.reshape(ny, nx), \n",
    "                       cmap='viridis', \n",
    "                       interpolation='none', \n",
    "                       origin='lower',\n",
    "                       vmin=_min, vmax=_max)\n",
    "    fig.colorbar(im, ax=axs[0])\n",
    "    axs[0].set_title(ttl1)  \n",
    "\n",
    "    im = axs[1].imshow(mean_post_pred_car.reshape(ny, nx), \n",
    "                       cmap='viridis', \n",
    "                       interpolation='none', \n",
    "                       origin='lower',\n",
    "                       vmin=_min, vmax=_max)\n",
    "\n",
    "    fig.colorbar(im, ax=axs[1])\n",
    "    axs[1].set_title(ttl2)\n",
    "    \n",
    "    im = axs[2].imshow(mean_post_pred_vae.reshape(ny, nx), \n",
    "                       cmap='viridis', \n",
    "                       interpolation='none', \n",
    "                       origin='lower',\n",
    "                       vmin=_min, vmax=_max)\n",
    "\n",
    "    fig.colorbar(im, ax=axs[2])\n",
    "    axs[2].set_title(ttl3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "341f4ebb",
   "metadata": {},
   "source": [
    "## Cimluate data based on the CAR model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "316f9e75",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "150\n"
     ]
    }
   ],
   "source": [
    "# create grid\n",
    "k = 1\n",
    "nx = 15 * k\n",
    "ny = 10 * k\n",
    "\n",
    "pols = [] # list of polygons\n",
    "\n",
    "for j in range(ny):\n",
    "    for i in range(nx):\n",
    "        coords = [(i,j), (i+1, j), (i+1, j+1), (i, j+1), (i,j)]\n",
    "        p = Polygon(coords)\n",
    "        pols.append(p)\n",
    "    \n",
    "N = len(pols)\n",
    "\n",
    "# adjacency matrix\n",
    "A = np.zeros(shape=(N,N))\n",
    "\n",
    "for i in range(N):\n",
    "    for j in range(i+1,N):\n",
    "        if (pols[i].intersection(pols[j]).length > 0):\n",
    "            A[i,j] = 1\n",
    "            A[j,i] = 1\n",
    "\n",
    "# number of neighbours\n",
    "d = A.sum(axis=0)\n",
    "\n",
    "#print(A)\n",
    "#print(d)\n",
    "print(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9c9197d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = jnp.diag(d)\n",
    "np.linalg.det(np.linalg.inv(D - A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "af787922",
   "metadata": {},
   "outputs": [],
   "source": [
    "def CAR(args):\n",
    "    \n",
    "    A = args[\"A\"]\n",
    "    d = args[\"d\"]\n",
    "    D = jnp.diag(d)\n",
    "\n",
    "    #alpha = numpyro.sample('alpha', dist.Uniform(low=0.01, high=0.999))\n",
    "    alpha = numpyro.sample('alpha', dist.Uniform(low=0.4, high=0.999))\n",
    "    \n",
    "    Q = (D - alpha * A)\n",
    "    \n",
    "    car = numpyro.sample('car', dist.MultivariateNormal(loc=jnp.zeros(N), precision_matrix=Q))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a0ac3f6a",
   "metadata": {},
   "outputs": [],
   "source": [
    "args = {# data\n",
    "        \"d\": d,\n",
    "        \"A\":A,\n",
    "        \"rng_key\": random.PRNGKey(0),\n",
    "        \"batch_size\": 100\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1e56e337",
   "metadata": {},
   "outputs": [],
   "source": [
    "# CAR: prior predictive\n",
    "\n",
    "rng_key = args[\"rng_key\"]\n",
    "rng_key, rng_key_ = random.split(rng_key)\n",
    "\n",
    "car_predictive = Predictive(CAR, num_samples=args[\"batch_size\"])\n",
    "car_preds = car_predictive(rng_key_, args)\n",
    "car_draws = car_preds['car']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3a62540e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1368x864 with 24 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_samps(car_draws)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa9e905f",
   "metadata": {},
   "source": [
    "## Train VAE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "cc3dd2e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "args = {# data\n",
    "        \"d\": d,\n",
    "        \"A\":A,\n",
    "        \"rng_key\": random.PRNGKey(0),\n",
    "    \n",
    "        # VAE training\n",
    "        \"num_epochs\": 300, \n",
    "        \"learning_rate\": 1.0e-3, \n",
    "        \"batch_size\": 100, \n",
    "        \"hidden_dim\": 130,\n",
    "        \"z_dim\": 130, \n",
    "        \"num_train\": 100,\n",
    "        \"num_test\":100,\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "67acc477",
   "metadata": {},
   "outputs": [],
   "source": [
    "def vae_encoder(hidden_dim, z_dim):\n",
    "    return stax.serial(\n",
    "        stax.Dense(hidden_dim, W_init=stax.randn()),\n",
    "        stax.Elu,\n",
    "        stax.FanOut(2),\n",
    "        stax.parallel(\n",
    "            stax.Dense(z_dim, W_init=stax.randn()), # mean\n",
    "            stax.serial(stax.Dense(z_dim, W_init=stax.randn()), stax.Exp), # std -- i.e. diagonal covariance\n",
    "        ),\n",
    "    )\n",
    "\n",
    "\n",
    "def vae_decoder( hidden_dim, out_dim):\n",
    "    return stax.serial(\n",
    "        stax.Dense(hidden_dim, W_init=stax.randn()),\n",
    "        stax.Elu,\n",
    "        stax.Dense(out_dim, W_init=stax.randn())\n",
    "    )\n",
    "\n",
    "def vae_model(batch, hidden_dim, z_dim):\n",
    "    batch = jnp.reshape(batch, (batch.shape[0], -1))\n",
    "    batch_dim, out_dim = jnp.shape(batch)\n",
    "    decode = numpyro.module(\"decoder\", vae_decoder( hidden_dim, out_dim), (batch_dim, z_dim))\n",
    "    z = numpyro.sample(\"z\", dist.Normal(jnp.zeros((z_dim,)), jnp.ones((z_dim,))))\n",
    "    gen_loc = decode(z)    \n",
    "    numpyro.sample(\"obs\", dist.Normal(gen_loc, .05), obs=batch) \n",
    "    #return \n",
    "    \n",
    "\n",
    "def vae_guide(batch, hidden_dim,  z_dim):\n",
    "    batch = jnp.reshape(batch, (batch.shape[0], -1))\n",
    "    batch_dim, out_dim = jnp.shape(batch)\n",
    "    encode = numpyro.module(\"encoder\", vae_encoder(hidden_dim, z_dim), (batch_dim, out_dim))\n",
    "    z_loc, z_std = encode(batch)\n",
    "    z = numpyro.sample(\"z\", dist.Normal(z_loc, z_std))\n",
    "    return z\n",
    "\n",
    "@jit\n",
    "def epoch_train(rng_key, svi_state, num_train):\n",
    "\n",
    "    def body_fn(i, val):\n",
    "        rng_key_i = random.fold_in(rng_key, i) \n",
    "        rng_key_i, rng_key_ls, rng_key_var, rng_key_noise = random.split(rng_key_i, 4)\n",
    "        loss_sum, svi_state = val # val -- svi_state\n",
    "        batch = car_predictive(rng_key_i, args)['car']\n",
    "        svi_state, loss = svi.update(svi_state, batch) \n",
    "        loss_sum += loss / args['batch_size']\n",
    "        return loss_sum, svi_state\n",
    "\n",
    "    return lax.fori_loop(0, num_train, body_fn, (0.0, svi_state)) #fori_loop(lower, upper, body_fun, init_val)\n",
    "\n",
    "@jit\n",
    "def eval_test(rng_key, svi_state, num_test):\n",
    "\n",
    "    def body_fn(i, loss_sum):\n",
    "        rng_key_i = random.fold_in(rng_key, i) \n",
    "        rng_key_i, rng_key_ls, rng_key_var, rng_key_noise = random.split(rng_key_i, 4)\n",
    "        batch = car_predictive(rng_key_i, args)['car']\n",
    "        loss = svi.evaluate(svi_state, batch) / args['batch_size']\n",
    "        loss_sum += loss\n",
    "        return loss_sum\n",
    "\n",
    "    loss = lax.fori_loop(0, num_test, body_fn, 0.0)\n",
    "    loss = loss / num_test\n",
    "\n",
    "    return loss\n",
    "\n",
    "adam = optim.Adam(step_size=args[\"learning_rate\"])\n",
    "\n",
    "#svi = SVI(vae_model, vae_guide, adam, RenyiELBO(alpha=-1, num_particles=4), \n",
    "svi = SVI(vae_model, vae_guide, adam, RenyiELBO(), \n",
    "          hidden_dim=args[\"hidden_dim\"], \n",
    "          z_dim=args[\"z_dim\"])\n",
    "\n",
    "rng_key, rng_key_samp, rng_key_init = random.split(args[\"rng_key\"], 3)\n",
    "init_batch = car_predictive(rng_key_, args)['car']\n",
    "svi_state = svi.init(rng_key_init, init_batch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7886b9d9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0: loss = 5634.044921875 (9.07 s.)\n",
      "Epoch 1: loss = 4273.1806640625 (0.00 s.)\n",
      "Epoch 2: loss = 3583.61572265625 (0.00 s.)\n",
      "Epoch 3: loss = 3228.06787109375 (0.00 s.)\n",
      "Epoch 4: loss = 2969.5390625 (0.00 s.)\n",
      "Epoch 5: loss = 2768.38232421875 (0.00 s.)\n",
      "Epoch 6: loss = 2604.810546875 (0.00 s.)\n",
      "Epoch 7: loss = 2497.6728515625 (0.00 s.)\n",
      "Epoch 8: loss = 2448.412353515625 (0.00 s.)\n",
      "Epoch 9: loss = 2348.6259765625 (0.00 s.)\n",
      "Epoch 10: loss = 2285.0146484375 (0.00 s.)\n",
      "Epoch 11: loss = 2200.13330078125 (0.00 s.)\n",
      "Epoch 12: loss = 2188.08837890625 (0.00 s.)\n",
      "Epoch 13: loss = 2136.335205078125 (0.00 s.)\n",
      "Epoch 14: loss = 2101.2724609375 (0.00 s.)\n",
      "Epoch 15: loss = 2048.6650390625 (0.00 s.)\n",
      "Epoch 16: loss = 2069.21337890625 (0.00 s.)\n",
      "Epoch 17: loss = 2044.8092041015625 (0.00 s.)\n",
      "Epoch 18: loss = 2000.8817138671875 (0.00 s.)\n",
      "Epoch 19: loss = 1989.5694580078125 (0.00 s.)\n",
      "Epoch 20: loss = 1951.499267578125 (0.00 s.)\n",
      "Epoch 21: loss = 1960.5921630859375 (0.00 s.)\n",
      "Epoch 22: loss = 1949.568603515625 (0.00 s.)\n",
      "Epoch 23: loss = 1907.457763671875 (0.00 s.)\n",
      "Epoch 24: loss = 1910.6402587890625 (0.00 s.)\n",
      "Epoch 25: loss = 1902.7283935546875 (0.00 s.)\n",
      "Epoch 26: loss = 1912.038330078125 (0.00 s.)\n",
      "Epoch 27: loss = 1907.275390625 (0.00 s.)\n",
      "Epoch 28: loss = 1896.948486328125 (0.00 s.)\n",
      "Epoch 29: loss = 1864.900634765625 (0.00 s.)\n",
      "Epoch 30: loss = 1858.9219970703125 (0.00 s.)\n",
      "Epoch 31: loss = 1855.683837890625 (0.00 s.)\n",
      "Epoch 32: loss = 1855.4100341796875 (0.00 s.)\n",
      "Epoch 33: loss = 1853.250732421875 (0.00 s.)\n",
      "Epoch 34: loss = 1817.336181640625 (0.00 s.)\n",
      "Epoch 35: loss = 1812.8436279296875 (0.00 s.)\n",
      "Epoch 36: loss = 1782.7041015625 (0.00 s.)\n",
      "Epoch 37: loss = 1777.501220703125 (0.00 s.)\n",
      "Epoch 38: loss = 1770.708984375 (0.00 s.)\n",
      "Epoch 39: loss = 1773.865234375 (0.00 s.)\n",
      "Epoch 40: loss = 1770.489013671875 (0.00 s.)\n",
      "Epoch 41: loss = 1770.3924560546875 (0.00 s.)\n",
      "Epoch 42: loss = 1777.5601806640625 (0.00 s.)\n",
      "Epoch 43: loss = 1765.66650390625 (0.00 s.)\n",
      "Epoch 44: loss = 1780.5582275390625 (0.00 s.)\n",
      "Epoch 45: loss = 1767.9473876953125 (0.00 s.)\n",
      "Epoch 46: loss = 1767.994140625 (0.00 s.)\n",
      "Epoch 47: loss = 1768.3424072265625 (0.00 s.)\n",
      "Epoch 48: loss = 1729.6124267578125 (0.00 s.)\n",
      "Epoch 49: loss = 1728.472900390625 (0.00 s.)\n",
      "Epoch 50: loss = 1729.7620849609375 (0.00 s.)\n",
      "Epoch 51: loss = 1727.58056640625 (0.00 s.)\n",
      "Epoch 52: loss = 1729.244140625 (0.00 s.)\n",
      "Epoch 53: loss = 1725.78173828125 (0.00 s.)\n",
      "Epoch 54: loss = 1729.654541015625 (0.00 s.)\n",
      "Epoch 55: loss = 1731.0367431640625 (0.00 s.)\n",
      "Epoch 56: loss = 1736.79443359375 (0.00 s.)\n",
      "Epoch 57: loss = 1727.0565185546875 (0.00 s.)\n",
      "Epoch 58: loss = 1731.8997802734375 (0.00 s.)\n",
      "Epoch 59: loss = 1733.3226318359375 (0.00 s.)\n",
      "Epoch 60: loss = 1725.9808349609375 (0.00 s.)\n",
      "Epoch 61: loss = 1724.784912109375 (0.00 s.)\n",
      "Epoch 62: loss = 1685.4791259765625 (0.00 s.)\n",
      "Epoch 63: loss = 1684.3553466796875 (0.00 s.)\n",
      "Epoch 64: loss = 1680.613037109375 (0.00 s.)\n",
      "Epoch 65: loss = 1696.338134765625 (0.00 s.)\n",
      "Epoch 66: loss = 1674.7362060546875 (0.00 s.)\n",
      "Epoch 67: loss = 1677.1064453125 (0.00 s.)\n",
      "Epoch 68: loss = 1681.829345703125 (0.00 s.)\n",
      "Epoch 69: loss = 1638.5794677734375 (0.00 s.)\n",
      "Epoch 70: loss = 1647.5538330078125 (0.00 s.)\n",
      "Epoch 71: loss = 1636.3277587890625 (0.00 s.)\n",
      "Epoch 72: loss = 1634.6981201171875 (0.00 s.)\n",
      "Epoch 73: loss = 1639.298583984375 (0.00 s.)\n",
      "Epoch 74: loss = 1643.1273193359375 (0.00 s.)\n",
      "Epoch 75: loss = 1634.781982421875 (0.00 s.)\n",
      "Epoch 76: loss = 1594.4503173828125 (0.00 s.)\n",
      "Epoch 77: loss = 1597.9229736328125 (0.00 s.)\n",
      "Epoch 78: loss = 1602.3265380859375 (0.00 s.)\n",
      "Epoch 79: loss = 1599.611572265625 (0.00 s.)\n",
      "Epoch 80: loss = 1603.924072265625 (0.00 s.)\n",
      "Epoch 81: loss = 1598.495361328125 (0.00 s.)\n",
      "Epoch 82: loss = 1603.73095703125 (0.00 s.)\n",
      "Epoch 83: loss = 1596.5706787109375 (0.00 s.)\n",
      "Epoch 84: loss = 1593.287109375 (0.00 s.)\n",
      "Epoch 85: loss = 1601.0162353515625 (0.00 s.)\n",
      "Epoch 86: loss = 1598.4208984375 (0.00 s.)\n",
      "Epoch 87: loss = 1619.1575927734375 (0.00 s.)\n",
      "Epoch 88: loss = 1595.498779296875 (0.00 s.)\n",
      "Epoch 89: loss = 1601.3778076171875 (0.00 s.)\n",
      "Epoch 90: loss = 1601.4791259765625 (0.00 s.)\n",
      "Epoch 91: loss = 1557.501708984375 (0.00 s.)\n",
      "Epoch 92: loss = 1556.474365234375 (0.00 s.)\n",
      "Epoch 93: loss = 1663.345947265625 (0.00 s.)\n",
      "Epoch 94: loss = 1692.1800537109375 (0.00 s.)\n",
      "Epoch 95: loss = 1587.5489501953125 (0.00 s.)\n",
      "Epoch 96: loss = 1521.118408203125 (0.00 s.)\n",
      "Epoch 97: loss = 1516.69140625 (0.00 s.)\n",
      "Epoch 98: loss = 1479.80322265625 (0.00 s.)\n",
      "Epoch 99: loss = 1526.2635498046875 (0.00 s.)\n",
      "Epoch 100: loss = 1453.22900390625 (0.00 s.)\n",
      "Epoch 101: loss = 1402.50927734375 (0.00 s.)\n",
      "Epoch 102: loss = 1392.9591064453125 (0.00 s.)\n",
      "Epoch 103: loss = 1398.357666015625 (0.00 s.)\n",
      "Epoch 104: loss = 1405.9735107421875 (0.00 s.)\n",
      "Epoch 105: loss = 1359.68212890625 (0.00 s.)\n",
      "Epoch 106: loss = 1353.98876953125 (0.00 s.)\n",
      "Epoch 107: loss = 1357.369384765625 (0.00 s.)\n",
      "Epoch 108: loss = 1322.737548828125 (0.00 s.)\n",
      "Epoch 109: loss = 1316.75830078125 (0.00 s.)\n",
      "Epoch 110: loss = 1323.0589599609375 (0.00 s.)\n",
      "Epoch 111: loss = 1314.8968505859375 (0.00 s.)\n",
      "Epoch 112: loss = 1321.9971923828125 (0.00 s.)\n",
      "Epoch 113: loss = 1278.1468505859375 (0.00 s.)\n",
      "Epoch 114: loss = 1280.4393310546875 (0.00 s.)\n",
      "Epoch 115: loss = 1278.2283935546875 (0.00 s.)\n",
      "Epoch 116: loss = 1270.9664306640625 (0.00 s.)\n",
      "Epoch 117: loss = 1273.00048828125 (0.00 s.)\n",
      "Epoch 118: loss = 1294.52099609375 (0.00 s.)\n",
      "Epoch 119: loss = 1274.9833984375 (0.00 s.)\n",
      "Epoch 120: loss = 1275.8875732421875 (0.00 s.)\n",
      "Epoch 121: loss = 1276.4114990234375 (0.00 s.)\n",
      "Epoch 122: loss = 1277.625732421875 (0.00 s.)\n",
      "Epoch 123: loss = 1276.4095458984375 (0.00 s.)\n",
      "Epoch 124: loss = 1275.9449462890625 (0.00 s.)\n",
      "Epoch 125: loss = 1283.53173828125 (0.00 s.)\n",
      "Epoch 126: loss = 1281.99365234375 (0.00 s.)\n",
      "Epoch 127: loss = 1274.3829345703125 (0.00 s.)\n",
      "Epoch 128: loss = 1275.0548095703125 (0.00 s.)\n",
      "Epoch 129: loss = 1272.1585693359375 (0.00 s.)\n",
      "Epoch 130: loss = 1287.099853515625 (0.00 s.)\n",
      "Epoch 131: loss = 1269.4697265625 (0.00 s.)\n",
      "Epoch 132: loss = 1274.0029296875 (0.00 s.)\n",
      "Epoch 133: loss = 1279.6632080078125 (0.00 s.)\n",
      "Epoch 134: loss = 1276.8736572265625 (0.00 s.)\n",
      "Epoch 135: loss = 1271.753173828125 (0.00 s.)\n",
      "Epoch 136: loss = 1272.3851318359375 (0.00 s.)\n",
      "Epoch 137: loss = 1269.9520263671875 (0.00 s.)\n",
      "Epoch 138: loss = 1274.505859375 (0.00 s.)\n",
      "Epoch 139: loss = 1273.392578125 (0.00 s.)\n",
      "Epoch 140: loss = 1276.965087890625 (0.00 s.)\n",
      "Epoch 141: loss = 1273.7945556640625 (0.00 s.)\n",
      "Epoch 142: loss = 1275.471923828125 (0.00 s.)\n",
      "Epoch 143: loss = 1281.385009765625 (0.00 s.)\n",
      "Epoch 144: loss = 1288.388671875 (0.00 s.)\n",
      "Epoch 145: loss = 1273.6048583984375 (0.00 s.)\n",
      "Epoch 146: loss = 1279.46875 (0.00 s.)\n",
      "Epoch 147: loss = 1277.9107666015625 (0.00 s.)\n",
      "Epoch 148: loss = 1279.239990234375 (0.00 s.)\n",
      "Epoch 149: loss = 1272.6143798828125 (0.00 s.)\n",
      "Epoch 150: loss = 1275.9619140625 (0.00 s.)\n",
      "Epoch 151: loss = 1274.191162109375 (0.00 s.)\n",
      "Epoch 152: loss = 1278.0091552734375 (0.00 s.)\n",
      "Epoch 153: loss = 1276.468994140625 (0.00 s.)\n",
      "Epoch 154: loss = 1283.7457275390625 (0.00 s.)\n",
      "Epoch 155: loss = 1274.944091796875 (0.00 s.)\n",
      "Epoch 156: loss = 1277.0272216796875 (0.00 s.)\n",
      "Epoch 157: loss = 1275.5189208984375 (0.00 s.)\n",
      "Epoch 158: loss = 1278.332275390625 (0.00 s.)\n",
      "Epoch 159: loss = 1278.076904296875 (0.00 s.)\n",
      "Epoch 160: loss = 1278.01904296875 (0.00 s.)\n",
      "Epoch 161: loss = 1276.45361328125 (0.00 s.)\n",
      "Epoch 162: loss = 1273.1085205078125 (0.00 s.)\n",
      "Epoch 163: loss = 1277.60693359375 (0.00 s.)\n",
      "Epoch 164: loss = 1277.394775390625 (0.00 s.)\n",
      "Epoch 165: loss = 1274.58740234375 (0.00 s.)\n",
      "Epoch 166: loss = 1272.84326171875 (0.00 s.)\n",
      "Epoch 167: loss = 1274.236328125 (0.00 s.)\n",
      "Epoch 168: loss = 1279.7958984375 (0.00 s.)\n",
      "Epoch 169: loss = 1274.6358642578125 (0.00 s.)\n",
      "Epoch 170: loss = 1271.4984130859375 (0.00 s.)\n",
      "Epoch 171: loss = 1277.48779296875 (0.00 s.)\n",
      "Epoch 172: loss = 1292.681640625 (0.00 s.)\n",
      "Epoch 173: loss = 1276.91064453125 (0.00 s.)\n",
      "Epoch 174: loss = 1274.6383056640625 (0.00 s.)\n",
      "Epoch 175: loss = 1277.374755859375 (0.00 s.)\n",
      "Epoch 176: loss = 1271.652587890625 (0.00 s.)\n",
      "Epoch 177: loss = 1270.9345703125 (0.00 s.)\n",
      "Epoch 178: loss = 1275.19189453125 (0.00 s.)\n",
      "Epoch 179: loss = 1281.4647216796875 (0.00 s.)\n",
      "Epoch 180: loss = 1271.98681640625 (0.00 s.)\n",
      "Epoch 181: loss = 1272.277099609375 (0.00 s.)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 182: loss = 1277.1546630859375 (0.00 s.)\n",
      "Epoch 183: loss = 1271.095947265625 (0.00 s.)\n",
      "Epoch 184: loss = 1279.5601806640625 (0.00 s.)\n",
      "Epoch 185: loss = 1280.3123779296875 (0.00 s.)\n",
      "Epoch 186: loss = 1276.583740234375 (0.00 s.)\n",
      "Epoch 187: loss = 1274.96240234375 (0.00 s.)\n",
      "Epoch 188: loss = 1274.767822265625 (0.00 s.)\n",
      "Epoch 189: loss = 1275.06201171875 (0.00 s.)\n",
      "Epoch 190: loss = 1282.250732421875 (0.00 s.)\n",
      "Epoch 191: loss = 1273.04345703125 (0.00 s.)\n",
      "Epoch 192: loss = 1271.357177734375 (0.00 s.)\n",
      "Epoch 193: loss = 1279.0694580078125 (0.00 s.)\n",
      "Epoch 194: loss = 1270.689697265625 (0.00 s.)\n",
      "Epoch 195: loss = 1270.0933837890625 (0.00 s.)\n",
      "Epoch 196: loss = 1279.171142578125 (0.00 s.)\n",
      "Epoch 197: loss = 1277.78466796875 (0.00 s.)\n",
      "Epoch 198: loss = 1278.245849609375 (0.00 s.)\n",
      "Epoch 199: loss = 1278.647216796875 (0.00 s.)\n",
      "Epoch 200: loss = 1276.016357421875 (0.00 s.)\n",
      "Epoch 201: loss = 1275.2967529296875 (0.00 s.)\n",
      "Epoch 202: loss = 1272.427978515625 (0.00 s.)\n",
      "Epoch 203: loss = 1276.553466796875 (0.00 s.)\n",
      "Epoch 204: loss = 1275.877685546875 (0.00 s.)\n",
      "Epoch 205: loss = 1278.609375 (0.00 s.)\n",
      "Epoch 206: loss = 1275.442626953125 (0.00 s.)\n",
      "Epoch 207: loss = 1268.666015625 (0.00 s.)\n",
      "Epoch 208: loss = 1271.77880859375 (0.00 s.)\n",
      "Epoch 209: loss = 1275.17041015625 (0.00 s.)\n",
      "Epoch 210: loss = 1273.68310546875 (0.00 s.)\n",
      "Epoch 211: loss = 1271.8658447265625 (0.00 s.)\n",
      "Epoch 212: loss = 1274.170654296875 (0.00 s.)\n",
      "Epoch 213: loss = 1276.0155029296875 (0.00 s.)\n",
      "Epoch 214: loss = 1273.396484375 (0.00 s.)\n",
      "Epoch 215: loss = 1270.1971435546875 (0.00 s.)\n",
      "Epoch 216: loss = 1272.699462890625 (0.00 s.)\n",
      "Epoch 217: loss = 1271.7962646484375 (0.00 s.)\n",
      "Epoch 218: loss = 1272.9271240234375 (0.00 s.)\n",
      "Epoch 219: loss = 1271.4913330078125 (0.00 s.)\n",
      "Epoch 220: loss = 1270.33203125 (0.00 s.)\n",
      "Epoch 221: loss = 1272.37890625 (0.00 s.)\n",
      "Epoch 222: loss = 1279.7862548828125 (0.00 s.)\n",
      "Epoch 223: loss = 1271.22509765625 (0.00 s.)\n",
      "Epoch 224: loss = 1272.115234375 (0.00 s.)\n",
      "Epoch 225: loss = 1287.2591552734375 (0.00 s.)\n",
      "Epoch 226: loss = 1273.47314453125 (0.00 s.)\n",
      "Epoch 227: loss = 1273.94775390625 (0.00 s.)\n",
      "Epoch 228: loss = 1273.7626953125 (0.00 s.)\n",
      "Epoch 229: loss = 1272.8695068359375 (0.00 s.)\n",
      "Epoch 230: loss = 1278.06982421875 (0.00 s.)\n",
      "Epoch 231: loss = 1272.847900390625 (0.00 s.)\n",
      "Epoch 232: loss = 1275.5523681640625 (0.00 s.)\n",
      "Epoch 233: loss = 1279.8111572265625 (0.00 s.)\n",
      "Epoch 234: loss = 1277.2598876953125 (0.00 s.)\n",
      "Epoch 235: loss = 1274.183349609375 (0.00 s.)\n",
      "Epoch 236: loss = 1272.6099853515625 (0.00 s.)\n",
      "Epoch 237: loss = 1273.140625 (0.00 s.)\n",
      "Epoch 238: loss = 1278.1295166015625 (0.00 s.)\n",
      "Epoch 239: loss = 1280.3458251953125 (0.00 s.)\n",
      "Epoch 240: loss = 1277.17041015625 (0.00 s.)\n",
      "Epoch 241: loss = 1276.5589599609375 (0.00 s.)\n",
      "Epoch 242: loss = 1269.5023193359375 (0.00 s.)\n",
      "Epoch 243: loss = 1277.8990478515625 (0.00 s.)\n",
      "Epoch 244: loss = 1282.6971435546875 (0.00 s.)\n",
      "Epoch 245: loss = 1267.5411376953125 (0.00 s.)\n",
      "Epoch 246: loss = 1235.992919921875 (0.00 s.)\n",
      "Epoch 247: loss = 1301.2939453125 (0.00 s.)\n",
      "Epoch 248: loss = 1234.891357421875 (0.00 s.)\n",
      "Epoch 249: loss = 1250.874755859375 (0.00 s.)\n",
      "Epoch 250: loss = 1234.291259765625 (0.00 s.)\n",
      "Epoch 251: loss = 1241.1002197265625 (0.00 s.)\n",
      "Epoch 252: loss = 1235.79052734375 (0.00 s.)\n",
      "Epoch 253: loss = 1236.5001220703125 (0.00 s.)\n",
      "Epoch 254: loss = 1239.8153076171875 (0.00 s.)\n",
      "Epoch 255: loss = 1243.54052734375 (0.00 s.)\n",
      "Epoch 256: loss = 1240.8228759765625 (0.00 s.)\n",
      "Epoch 257: loss = 1235.4510498046875 (0.00 s.)\n",
      "Epoch 258: loss = 1234.0888671875 (0.00 s.)\n",
      "Epoch 259: loss = 1239.8802490234375 (0.00 s.)\n",
      "Epoch 260: loss = 1233.2762451171875 (0.00 s.)\n",
      "Epoch 261: loss = 1231.5709228515625 (0.00 s.)\n",
      "Epoch 262: loss = 1238.7293701171875 (0.00 s.)\n",
      "Epoch 263: loss = 1230.769287109375 (0.00 s.)\n",
      "Epoch 264: loss = 1237.4403076171875 (0.00 s.)\n",
      "Epoch 265: loss = 1235.2822265625 (0.00 s.)\n",
      "Epoch 266: loss = 1232.544189453125 (0.00 s.)\n",
      "Epoch 267: loss = 1239.8167724609375 (0.00 s.)\n",
      "Epoch 268: loss = 1237.12255859375 (0.00 s.)\n",
      "Epoch 269: loss = 1233.6771240234375 (0.00 s.)\n",
      "Epoch 270: loss = 1241.8121337890625 (0.00 s.)\n",
      "Epoch 271: loss = 1233.113525390625 (0.00 s.)\n",
      "Epoch 272: loss = 1233.9530029296875 (0.00 s.)\n",
      "Epoch 273: loss = 1237.2911376953125 (0.00 s.)\n",
      "Epoch 274: loss = 1239.14697265625 (0.00 s.)\n",
      "Epoch 275: loss = 1238.3302001953125 (0.00 s.)\n",
      "Epoch 276: loss = 1239.0364990234375 (0.00 s.)\n",
      "Epoch 277: loss = 1241.5347900390625 (0.00 s.)\n",
      "Epoch 278: loss = 1234.978759765625 (0.00 s.)\n",
      "Epoch 279: loss = 1237.6314697265625 (0.00 s.)\n",
      "Epoch 280: loss = 1231.5391845703125 (0.00 s.)\n",
      "Epoch 281: loss = 1236.745361328125 (0.00 s.)\n",
      "Epoch 282: loss = 1233.5218505859375 (0.00 s.)\n",
      "Epoch 283: loss = 1238.4632568359375 (0.00 s.)\n",
      "Epoch 284: loss = 1237.717041015625 (0.00 s.)\n",
      "Epoch 285: loss = 1235.111572265625 (0.00 s.)\n",
      "Epoch 286: loss = 1236.9952392578125 (0.00 s.)\n",
      "Epoch 287: loss = 1240.239501953125 (0.00 s.)\n",
      "Epoch 288: loss = 1232.0712890625 (0.00 s.)\n",
      "Epoch 289: loss = 1236.819580078125 (0.00 s.)\n",
      "Epoch 290: loss = 1233.357666015625 (0.00 s.)\n",
      "Epoch 291: loss = 1238.1309814453125 (0.00 s.)\n",
      "Epoch 292: loss = 1237.348388671875 (0.00 s.)\n",
      "Epoch 293: loss = 1234.5833740234375 (0.00 s.)\n",
      "Epoch 294: loss = 1236.0721435546875 (0.00 s.)\n",
      "Epoch 295: loss = 1242.2120361328125 (0.00 s.)\n",
      "Epoch 296: loss = 1240.076904296875 (0.00 s.)\n",
      "Epoch 297: loss = 1236.720703125 (0.00 s.)\n",
      "Epoch 298: loss = 1237.763916015625 (0.00 s.)\n",
      "Epoch 299: loss = 1231.555908203125 (0.00 s.)\n"
     ]
    }
   ],
   "source": [
    "test_loss_list = []\n",
    "\n",
    "for i in range(args['num_epochs']):\n",
    "    \n",
    "    rng_key, rng_key_train, rng_key_test, rng_key_infer = random.split(rng_key, 4)\n",
    "    \n",
    "    t_start = time.time()\n",
    "\n",
    "    num_train = 1000\n",
    "    _, svi_state = epoch_train(rng_key_train, svi_state, num_train)\n",
    "\n",
    "    num_test = 1000\n",
    "    test_loss = eval_test(rng_key_test, svi_state, num_test)\n",
    "    test_loss_list += [test_loss]\n",
    "\n",
    "    print(\"Epoch {}: loss = {} ({:.2f} s.)\".format(i, test_loss, time.time() - t_start))\n",
    "    \n",
    "    if math.isnan(test_loss): break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "0a6f9e86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(np.arange(0, len(test_loss_list), 1), test_loss_list, label=\"test loss\")\n",
    "plt.xlabel(\"epochs\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "728b1877",
   "metadata": {},
   "outputs": [],
   "source": [
    "decoder_params = svi.get_params(svi_state)[\"decoder$params\"]\n",
    "args[\"decoder_params\"] = decoder_params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "a064737b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save after training\n",
    "#with open('decoders/decoder_car_sim', 'wb') as file:\n",
    "#    pickle.dump(decoder_params, file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "27bc94a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load \n",
    "#with open('../decoders/decoder_car_sim', 'rb') as file:\n",
    "#    decoder_params = pickle.load(file)\n",
    "#    print(len(decoder_params))\n",
    "\n",
    "#args[\"decoder_params\"] = decoder_params"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea9ad178",
   "metadata": {},
   "source": [
    "## Plot what VAE has learnt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "c4f6568a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.67465043 -0.31698686 -0.93045545 -1.2586647 ]\n",
      "[-1.1607877 -0.6851652 -1.9321165 -2.2778022]\n",
      "[-1.4917748 -1.0985749 -2.9038036 -3.0696547]\n",
      "[-1.7153201 -1.536747  -3.8144243 -3.7189057]\n",
      "[-1.8854735 -1.9842002 -4.6707172 -4.2823997]\n",
      "[-2.0248349 -2.4335902 -5.480474  -4.795073 ]\n",
      "[-2.1454961 -2.882787  -6.250515  -5.27703  ]\n",
      "[-2.2547746 -3.3305078 -6.988548  -5.739807 ]\n",
      "[-2.3569326 -3.7760715 -7.7006702 -6.190615 ]\n",
      "[-2.455011  -4.2192144 -8.392093  -6.6339235]\n"
     ]
    }
   ],
   "source": [
    "decoder_params = args[\"decoder_params\"] \n",
    "z_dim, hidden_dim = decoder_params[0][0].shape\n",
    "    \n",
    "decoder_nn = vae_decoder(hidden_dim, N)  \n",
    "\n",
    "# check output of the decoder\n",
    "for i in range(10):\n",
    "    z = jnp.ones(z_dim) + i\n",
    "    print(decoder_nn[1](decoder_params, z)[0:4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "19501d5d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def vae_sample(args):\n",
    "    \n",
    "    decoder_params = args[\"decoder_params\"] \n",
    "    z_dim, hidden_dim = decoder_params[0][0].shape\n",
    "    \n",
    "    z = numpyro.sample(\"z\", dist.Normal(jnp.zeros(z_dim), jnp.ones(z_dim)))\n",
    "    decoder_nn = vae_decoder( hidden_dim, N)  \n",
    "    car = numpyro.deterministic(\"car\", decoder_nn[1](decoder_params, z)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "413d6733",
   "metadata": {},
   "outputs": [],
   "source": [
    "rng_key, rng_key_predict = random.split(random.PRNGKey(2))\n",
    "vae_predictive = Predictive(vae_sample, num_samples=12)\n",
    "vae_draws = vae_predictive(rng_key_predict, args)['car']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "0897a49d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1368x432 with 16 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1368x432 with 16 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_samps(car_draws, columns=4, rows=2, figsize = (19, 6))\n",
    "plot_samps(vae_draws, columns=4, rows=2, figsize = (19, 6), ttl=\"VAE learnt priors\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "a574f25c",
   "metadata": {},
   "outputs": [],
   "source": [
    "#plot_car(car_draws)\n",
    "#plot_car(vae_draws, ttl=\"VAE learnt priors\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0c1791e",
   "metadata": {},
   "source": [
    "## Inference on observed data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "dfba10bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def CAR_model(args, y=None, alpha=None, noise=None):\n",
    "    \n",
    "    A = args[\"A\"]\n",
    "    d = args[\"d\"]\n",
    "    D = jnp.diag(d)\n",
    "\n",
    "    if alpha is None:\n",
    "        alpha = numpyro.sample('alpha', dist.Uniform(low=0.4, high=0.999))\n",
    "        \n",
    "    if noise is None:\n",
    "        noise = numpyro.sample('noise', dist.Uniform(low=0.01, high=1))\n",
    "    \n",
    "    Q = (D - alpha * A)\n",
    "    \n",
    "    car = numpyro.sample('car', dist.MultivariateNormal(loc=jnp.zeros(N), precision_matrix=Q))\n",
    "    car_samples = numpyro.deterministic('car_samples', car)\n",
    "    \n",
    "    if y is None: # durinig prediction\n",
    "        numpyro.sample(\"y_pred\", dist.Normal(car, noise))\n",
    "    else: # during inference\n",
    "        numpyro.sample(\"y\", dist.Normal(car, noise), obs=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "60bbe593",
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate ground truth - fix alpha\n",
    "rng_key, rng_key_truth = random.split(rng_key)\n",
    "car_predictive = Predictive(CAR_model, num_samples=1)\n",
    "car_preds = car_predictive(rng_key_truth, args, alpha=0.7, noise=0.5)\n",
    "y_data = car_preds['y_pred'][0,:]\n",
    "y_truth = car_preds['car'][0,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "8d997f3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_truth_estimate(y_truth, y_data, ttl1=\"truth\", ttl2=\"data (truth + noise)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "72e17293",
   "metadata": {},
   "outputs": [],
   "source": [
    "#plt.figure()\n",
    "#plt.imshow(y_true.reshape(ny, nx)) \n",
    "#plt.title(\"Ground Truth\")\n",
    "#plt.colorbar(shrink = 0.4)\n",
    "#plt.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60eef257",
   "metadata": {},
   "source": [
    "## Inference with VAE-CAR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "26fc3254",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "150"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "0816cb97",
   "metadata": {},
   "outputs": [],
   "source": [
    "def VAE_model(args, y=None, noise=None):\n",
    "    \n",
    "    decoder_params = args[\"decoder_params\"] \n",
    "    z_dim, hidden_dim = decoder_params[0][0].shape\n",
    "    z = numpyro.sample(\"z\", dist.Normal(jnp.zeros(z_dim), jnp.ones(z_dim)))\n",
    "    decoder_nn = vae_decoder( hidden_dim, N)  \n",
    "    car_vae = numpyro.deterministic(\"vae_car\", decoder_nn[1](decoder_params, z))\n",
    "    \n",
    "    if noise is None:\n",
    "        noise = numpyro.sample('noise', dist.Uniform(low=0.01, high=1))\n",
    "    \n",
    "    if y is None: # durinig prediction\n",
    "        numpyro.sample(\"y_pred\", dist.Normal(car_vae, noise))\n",
    "    else: # during inference\n",
    "        numpyro.sample(\"y\", dist.Normal(car_vae, noise), obs=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "3c7c37c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# VAE-CAR: prior predictive\n",
    "rng_key, rng_key_ = random.split(rng_key)\n",
    "prior_predictive = Predictive(VAE_model, num_samples=100)\n",
    "prior_predictions = prior_predictive(rng_key_, args)\n",
    "pred_obs = prior_predictions['vae_car']\n",
    "mean_prior_pred_vae = np.mean(pred_obs, axis=0)\n",
    "hpdi_prior_pred_vae = hpdi(pred_obs, 0.89)\n",
    "\n",
    "plt.figure()\n",
    "plt.imshow(mean_prior_pred_vae.reshape(ny, nx)) \n",
    "plt.colorbar(shrink=0.4)\n",
    "plt.title(\"VAE-CAR prior\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "2ab641bc",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "sample: 100%|██████████████████████████████████████████████| 3000/3000 [00:04<00:00, 727.98it/s, 15 steps of size 3.65e-01. acc. prob=0.87]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                  mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
      "       noise      0.53      0.05      0.52      0.45      0.60   1158.87      1.00\n",
      "  vae_car[0]     -0.67      0.45     -0.68     -1.47      0.02   4839.26      1.00\n",
      "  vae_car[1]      0.34      0.41      0.34     -0.31      1.04   5265.48      1.00\n",
      "  vae_car[2]      0.69      0.42      0.69     -0.00      1.36   4581.99      1.00\n",
      "  vae_car[3]      0.41      0.41      0.40     -0.27      1.05   5528.55      1.00\n",
      "  vae_car[4]     -0.75      0.40     -0.74     -1.38     -0.08   4877.02      1.00\n",
      "  vae_car[5]     -0.75      0.42     -0.76     -1.41     -0.06   4994.66      1.00\n",
      "  vae_car[6]     -0.82      0.41     -0.81     -1.47     -0.15   7405.93      1.00\n",
      "  vae_car[7]     -0.88      0.41     -0.89     -1.56     -0.24   5150.29      1.00\n",
      "  vae_car[8]     -0.17      0.39     -0.17     -0.80      0.47   4527.08      1.00\n",
      "  vae_car[9]      0.63      0.42      0.64     -0.08      1.29   4138.75      1.00\n",
      " vae_car[10]     -0.27      0.40     -0.27     -0.92      0.36   4361.07      1.00\n",
      " vae_car[11]     -0.23      0.40     -0.23     -0.86      0.46   4039.05      1.00\n",
      " vae_car[12]      0.22      0.40      0.22     -0.41      0.89   3884.46      1.00\n",
      " vae_car[13]     -0.50      0.40     -0.49     -1.10      0.22   5732.24      1.00\n",
      " vae_car[14]     -0.50      0.44     -0.50     -1.26      0.18   4856.24      1.00\n",
      " vae_car[15]     -0.39      0.40     -0.40     -1.01      0.32   4924.77      1.00\n",
      " vae_car[16]     -0.18      0.32     -0.19     -0.73      0.33   4978.44      1.00\n",
      " vae_car[17]     -0.10      0.34     -0.11     -0.65      0.45   5141.83      1.00\n",
      " vae_car[18]     -0.15      0.33     -0.15     -0.72      0.38   4021.03      1.00\n",
      " vae_car[19]     -0.34      0.35     -0.33     -0.90      0.23   4788.47      1.00\n",
      " vae_car[20]     -0.33      0.34     -0.33     -0.89      0.20   4367.28      1.00\n",
      " vae_car[21]     -0.43      0.33     -0.43     -0.97      0.06   4302.37      1.00\n",
      " vae_car[22]     -0.30      0.34     -0.31     -0.87      0.25   4380.36      1.00\n",
      " vae_car[23]     -0.10      0.36     -0.12     -0.62      0.54   5932.25      1.00\n",
      " vae_car[24]      0.02      0.34      0.03     -0.55      0.57   3961.86      1.00\n",
      " vae_car[25]     -0.71      0.35     -0.70     -1.22     -0.09   4403.31      1.00\n",
      " vae_car[26]     -0.18      0.35     -0.17     -0.71      0.42   6887.27      1.00\n",
      " vae_car[27]     -0.26      0.34     -0.26     -0.82      0.28   9093.33      1.00\n",
      " vae_car[28]     -0.92      0.32     -0.93     -1.44     -0.38   4406.08      1.00\n",
      " vae_car[29]     -0.89      0.41     -0.88     -1.58     -0.25   5943.47      1.00\n",
      " vae_car[30]     -0.64      0.40     -0.62     -1.31      0.00   4052.13      1.00\n",
      " vae_car[31]     -0.23      0.35     -0.24     -0.77      0.36   5765.33      1.00\n",
      " vae_car[32]      0.11      0.36      0.12     -0.51      0.67   5781.82      1.00\n",
      " vae_car[33]     -0.19      0.37     -0.18     -0.82      0.38   4640.92      1.00\n",
      " vae_car[34]      0.51      0.36      0.52     -0.05      1.11   4824.58      1.00\n",
      " vae_car[35]      0.93      0.37      0.94      0.29      1.52   4806.06      1.00\n",
      " vae_car[36]      0.10      0.34      0.10     -0.45      0.65   5537.58      1.00\n",
      " vae_car[37]     -0.02      0.35     -0.01     -0.61      0.55   4074.64      1.00\n",
      " vae_car[38]     -0.44      0.35     -0.44     -1.02      0.16   5871.33      1.00\n",
      " vae_car[39]     -0.36      0.33     -0.35     -0.90      0.19   4085.66      1.00\n",
      " vae_car[40]     -1.18      0.36     -1.18     -1.78     -0.58   5147.97      1.00\n",
      " vae_car[41]     -1.12      0.35     -1.13     -1.67     -0.52   4840.05      1.00\n",
      " vae_car[42]     -1.25      0.35     -1.26     -1.84     -0.68   4102.44      1.00\n",
      " vae_car[43]     -1.50      0.35     -1.50     -2.07     -0.91   3085.55      1.00\n",
      " vae_car[44]     -1.05      0.41     -1.05     -1.77     -0.44   5669.79      1.00\n",
      " vae_car[45]     -0.77      0.44     -0.78     -1.48     -0.10   3710.86      1.00\n",
      " vae_car[46]     -0.25      0.35     -0.25     -0.81      0.32   3778.88      1.00\n",
      " vae_car[47]      0.26      0.35      0.27     -0.31      0.83   4280.45      1.00\n",
      " vae_car[48]     -0.20      0.34     -0.21     -0.81      0.34   4985.02      1.00\n",
      " vae_car[49]      0.34      0.34      0.34     -0.25      0.87   4221.83      1.00\n",
      " vae_car[50]      0.45      0.35      0.45     -0.13      0.97   5536.82      1.00\n",
      " vae_car[51]     -0.56      0.36     -0.57     -1.12      0.03   4592.71      1.00\n",
      " vae_car[52]     -0.81      0.35     -0.82     -1.41     -0.28   4910.15      1.00\n",
      " vae_car[53]     -0.72      0.33     -0.72     -1.24     -0.17   4270.72      1.00\n",
      " vae_car[54]     -0.05      0.34     -0.05     -0.62      0.48   3732.32      1.00\n",
      " vae_car[55]     -0.76      0.34     -0.76     -1.30     -0.19   4587.40      1.00\n",
      " vae_car[56]     -0.93      0.33     -0.93     -1.49     -0.42   4359.35      1.00\n",
      " vae_car[57]     -1.01      0.33     -1.01     -1.54     -0.46   5038.25      1.00\n",
      " vae_car[58]     -0.92      0.34     -0.92     -1.47     -0.37   4742.12      1.00\n",
      " vae_car[59]     -0.77      0.39     -0.78     -1.38     -0.11   5775.66      1.00\n",
      " vae_car[60]     -0.56      0.42     -0.55     -1.23      0.10   4158.67      1.00\n",
      " vae_car[61]     -0.40      0.35     -0.41     -0.98      0.18   4662.96      1.00\n",
      " vae_car[62]      0.54      0.37      0.54     -0.06      1.16   4939.88      1.00\n",
      " vae_car[63]      0.38      0.36      0.38     -0.21      0.96   5020.44      1.00\n",
      " vae_car[64]      0.63      0.35      0.63      0.11      1.22   5007.64      1.00\n",
      " vae_car[65]      0.71      0.35      0.71      0.13      1.25   4215.17      1.00\n",
      " vae_car[66]      0.08      0.34      0.08     -0.46      0.68   5239.38      1.00\n",
      " vae_car[67]     -0.10      0.35     -0.10     -0.70      0.45   5833.04      1.00\n",
      " vae_car[68]     -0.03      0.34     -0.04     -0.59      0.54   4943.11      1.00\n",
      " vae_car[69]      0.46      0.35      0.46     -0.13      1.02   4340.05      1.00\n",
      " vae_car[70]     -0.26      0.37     -0.27     -0.84      0.33   4442.35      1.00\n",
      " vae_car[71]     -0.80      0.34     -0.80     -1.36     -0.24   4684.27      1.00\n",
      " vae_car[72]     -0.73      0.34     -0.74     -1.25     -0.14   4340.62      1.00\n",
      " vae_car[73]     -0.64      0.33     -0.64     -1.18     -0.11   5137.16      1.00\n",
      " vae_car[74]     -0.42      0.41     -0.42     -1.02      0.31   4449.93      1.00\n",
      " vae_car[75]      0.34      0.41      0.34     -0.34      0.98   4032.57      1.00\n",
      " vae_car[76]      0.46      0.32      0.46     -0.08      0.96   4192.00      1.00\n",
      " vae_car[77]      0.92      0.35      0.92      0.37      1.52   4832.09      1.00\n",
      " vae_car[78]      0.06      0.35      0.06     -0.51      0.65   3749.28      1.00\n",
      " vae_car[79]     -0.04      0.35     -0.03     -0.61      0.52   4446.94      1.00\n",
      " vae_car[80]      0.56      0.34      0.55      0.06      1.16   4971.04      1.00\n",
      " vae_car[81]      0.69      0.35      0.69      0.14      1.25   5526.29      1.00\n",
      " vae_car[82]      0.37      0.35      0.37     -0.19      0.94   4391.65      1.00\n",
      " vae_car[83]     -0.07      0.34     -0.08     -0.61      0.52   5547.34      1.00\n",
      " vae_car[84]     -0.17      0.34     -0.16     -0.75      0.34   5181.88      1.00\n",
      " vae_car[85]     -0.38      0.34     -0.38     -0.97      0.17   4500.03      1.00\n",
      " vae_car[86]     -0.45      0.33     -0.44     -0.98      0.12   5527.83      1.00\n",
      " vae_car[87]      0.11      0.34      0.11     -0.46      0.66   4978.73      1.00\n",
      " vae_car[88]     -0.07      0.33     -0.06     -0.60      0.46   4324.26      1.00\n",
      " vae_car[89]     -0.25      0.43     -0.25     -0.93      0.46   4167.21      1.00\n",
      " vae_car[90]     -0.21      0.41     -0.21     -0.92      0.42   4483.55      1.00\n",
      " vae_car[91]      0.37      0.33      0.37     -0.14      0.93   3712.74      1.00\n",
      " vae_car[92]      0.95      0.35      0.96      0.39      1.53   4588.85      1.00\n",
      " vae_car[93]     -0.11      0.34     -0.12     -0.66      0.42   5052.13      1.00\n",
      " vae_car[94]     -0.21      0.35     -0.21     -0.79      0.38   4963.01      1.00\n",
      " vae_car[95]      0.38      0.34      0.38     -0.22      0.91   5721.85      1.00\n",
      " vae_car[96]      0.38      0.33      0.38     -0.13      0.94   5144.01      1.00\n",
      " vae_car[97]      0.30      0.35      0.30     -0.23      0.92   4450.01      1.00\n",
      " vae_car[98]      0.22      0.36      0.22     -0.33      0.82   5641.07      1.00\n",
      " vae_car[99]     -0.08      0.34     -0.08     -0.61      0.51   4427.89      1.00\n",
      "vae_car[100]     -0.36      0.34     -0.37     -0.88      0.20   4398.66      1.00\n",
      "vae_car[101]     -0.48      0.34     -0.47     -1.04      0.06   4875.07      1.00\n",
      "vae_car[102]      0.25      0.35      0.25     -0.26      0.89   4517.28      1.00\n",
      "vae_car[103]      0.17      0.33      0.18     -0.39      0.72   4033.87      1.00\n",
      "vae_car[104]      0.53      0.40      0.52     -0.14      1.17   6395.91      1.00\n",
      "vae_car[105]      0.98      0.40      0.99      0.31      1.64   4772.67      1.00\n",
      "vae_car[106]     -0.18      0.33     -0.18     -0.72      0.34   4022.38      1.00\n",
      "vae_car[107]     -0.06      0.37     -0.06     -0.71      0.50   4192.95      1.00\n",
      "vae_car[108]     -0.23      0.35     -0.24     -0.76      0.39   4605.93      1.00\n",
      "vae_car[109]      0.23      0.35      0.23     -0.33      0.82   4979.43      1.00\n",
      "vae_car[110]      0.51      0.34      0.51     -0.02      1.08   3828.91      1.00\n",
      "vae_car[111]      0.06      0.35      0.06     -0.51      0.66   5165.68      1.00\n",
      "vae_car[112]     -0.11      0.33     -0.12     -0.66      0.42   3125.74      1.00\n",
      "vae_car[113]      0.34      0.34      0.34     -0.25      0.87   4510.83      1.00\n",
      "vae_car[114]      0.14      0.34      0.14     -0.44      0.69   3958.32      1.00\n",
      "vae_car[115]      0.03      0.35      0.03     -0.55      0.59   6646.82      1.00\n",
      "vae_car[116]     -0.44      0.36     -0.44     -1.02      0.13   5041.74      1.00\n",
      "vae_car[117]     -0.05      0.35     -0.05     -0.63      0.52   4143.53      1.00\n",
      "vae_car[118]      0.02      0.33      0.02     -0.51      0.56   4685.53      1.00\n",
      "vae_car[119]      0.51      0.40      0.51     -0.13      1.17   4663.50      1.00\n",
      "vae_car[120]      0.22      0.41      0.21     -0.43      0.90   4613.79      1.00\n",
      "vae_car[121]     -0.54      0.32     -0.54     -1.06     -0.03   3977.12      1.00\n",
      "vae_car[122]     -0.37      0.34     -0.37     -0.97      0.12   4927.58      1.00\n",
      "vae_car[123]     -0.04      0.33     -0.04     -0.59      0.48   3719.13      1.00\n",
      "vae_car[124]      0.20      0.35      0.20     -0.36      0.79   4418.24      1.00\n",
      "vae_car[125]      0.30      0.35      0.29     -0.27      0.86   4194.33      1.00\n",
      "vae_car[126]      0.26      0.34      0.26     -0.30      0.84   7010.08      1.00\n",
      "vae_car[127]      0.14      0.35      0.15     -0.42      0.69   4760.87      1.00\n",
      "vae_car[128]      0.37      0.34      0.37     -0.15      0.93   4596.10      1.00\n",
      "vae_car[129]     -0.15      0.35     -0.15     -0.72      0.39   4948.33      1.00\n",
      "vae_car[130]     -0.15      0.34     -0.15     -0.72      0.44   5483.07      1.00\n",
      "vae_car[131]     -0.24      0.34     -0.24     -0.78      0.34   4001.06      1.00\n",
      "vae_car[132]      0.33      0.35      0.33     -0.24      0.92   4300.24      1.00\n",
      "vae_car[133]      0.17      0.34      0.17     -0.42      0.70   4223.99      1.00\n",
      "vae_car[134]     -0.37      0.41     -0.38     -1.05      0.27   4675.46      1.00\n",
      "vae_car[135]     -0.03      0.42     -0.03     -0.68      0.67   3640.98      1.00\n",
      "vae_car[136]     -0.17      0.41     -0.17     -0.81      0.51   5907.34      1.00\n",
      "vae_car[137]     -0.58      0.40     -0.59     -1.22      0.11   5539.05      1.00\n",
      "vae_car[138]     -0.59      0.39     -0.59     -1.20      0.10   3821.94      1.00\n",
      "vae_car[139]      0.02      0.41      0.01     -0.66      0.72   5148.20      1.00\n",
      "vae_car[140]      0.54      0.42      0.52     -0.14      1.21   3878.66      1.00\n",
      "vae_car[141]      0.73      0.41      0.73      0.06      1.38   3927.93      1.00\n",
      "vae_car[142]      0.02      0.40      0.01     -0.68      0.62   6828.36      1.00\n",
      "vae_car[143]     -0.01      0.40     -0.01     -0.64      0.68   5950.96      1.00\n",
      "vae_car[144]     -0.67      0.40     -0.67     -1.34     -0.04   3899.57      1.00\n",
      "vae_car[145]     -0.52      0.41     -0.53     -1.18      0.17   4606.55      1.00\n",
      "vae_car[146]     -0.32      0.41     -0.31     -0.97      0.36   4432.99      1.00\n",
      "vae_car[147]      0.34      0.41      0.33     -0.31      1.03   3728.93      1.00\n",
      "vae_car[148]      0.37      0.41      0.38     -0.30      1.02   4392.83      1.00\n",
      "vae_car[149]     -0.49      0.43     -0.49     -1.24      0.17   4794.83      1.00\n",
      "        z[0]      0.82      0.67      0.83     -0.27      1.92   4747.14      1.00\n",
      "        z[1]     -0.65      0.69     -0.63     -1.88      0.36   4802.27      1.00\n",
      "        z[2]      0.83      0.59      0.85     -0.16      1.79   3826.81      1.00\n",
      "        z[3]      0.11      0.63      0.10     -0.92      1.13   5481.90      1.00\n",
      "        z[4]     -0.54      0.38     -0.54     -1.19      0.04   4731.22      1.00\n",
      "        z[5]      0.08      0.69      0.07     -1.00      1.27   5208.06      1.00\n",
      "        z[6]      1.11      0.35      1.11      0.57      1.67   3729.57      1.00\n",
      "        z[7]      0.26      0.68      0.26     -0.74      1.53   4368.52      1.00\n",
      "        z[8]     -0.00      0.97      0.02     -1.67      1.48   5514.09      1.00\n",
      "        z[9]     -0.13      0.69     -0.13     -1.25      1.02   4976.05      1.00\n",
      "       z[10]      0.43      0.71      0.43     -0.72      1.62   3939.23      1.00\n",
      "       z[11]     -0.62      0.67     -0.62     -1.65      0.47   5087.56      1.00\n",
      "       z[12]     -0.53      0.57     -0.53     -1.47      0.39   3813.23      1.00\n",
      "       z[13]      0.35      0.58      0.35     -0.60      1.30   5392.27      1.00\n",
      "       z[14]      0.02      1.00      0.02     -1.57      1.59   5061.23      1.00\n",
      "       z[15]      0.37      0.65      0.39     -0.69      1.40   4545.76      1.00\n",
      "       z[16]      0.76      0.28      0.76      0.30      1.23   3719.56      1.00\n",
      "       z[17]     -0.23      0.66     -0.24     -1.37      0.79   5305.96      1.00\n",
      "       z[18]      0.49      0.64      0.50     -0.55      1.52   4026.73      1.00\n",
      "       z[19]     -0.02      1.02     -0.00     -1.69      1.65   4122.51      1.00\n",
      "       z[20]     -0.57      0.51     -0.58     -1.39      0.25   5217.43      1.00\n",
      "       z[21]     -0.85      0.71     -0.85     -1.94      0.39   3981.68      1.00\n",
      "       z[22]      0.83      0.74      0.85     -0.28      2.11   4548.40      1.00\n",
      "       z[23]     -0.18      0.66     -0.20     -1.23      0.91   4362.99      1.00\n",
      "       z[24]     -0.71      0.64     -0.71     -1.71      0.34   4446.74      1.00\n",
      "       z[25]     -0.58      0.56     -0.60     -1.45      0.40   3413.02      1.00\n",
      "       z[26]      0.03      0.61      0.02     -0.89      1.09   4748.45      1.00\n",
      "       z[27]      0.15      0.52      0.15     -0.70      0.96   4707.29      1.00\n",
      "       z[28]     -0.27      0.49     -0.27     -1.03      0.55   6940.55      1.00\n",
      "       z[29]      0.27      0.65      0.28     -0.82      1.30   5244.93      1.00\n",
      "       z[30]     -0.31      0.70     -0.31     -1.49      0.78   4141.90      1.00\n",
      "       z[31]      0.62      0.55      0.62     -0.26      1.47   4069.64      1.00\n",
      "       z[32]     -1.63      0.55     -1.63     -2.51     -0.71   4342.37      1.00\n",
      "       z[33]     -0.17      0.70     -0.15     -1.34      0.94   3938.81      1.00\n",
      "       z[34]      0.78      0.62      0.79     -0.27      1.75   4004.36      1.00\n",
      "       z[35]      1.13      0.65      1.14      0.14      2.25   4838.13      1.00\n",
      "       z[36]      0.15      0.66      0.14     -0.92      1.22   5038.99      1.00\n",
      "       z[37]      0.08      0.69      0.09     -1.07      1.19   4937.32      1.00\n",
      "       z[38]     -0.23      0.40     -0.22     -0.87      0.44   4042.73      1.00\n",
      "       z[39]     -0.06      0.68     -0.06     -1.17      1.09   5687.31      1.00\n",
      "       z[40]     -1.06      0.68     -1.05     -2.15      0.07   4142.70      1.00\n",
      "       z[41]     -0.64      0.65     -0.63     -1.67      0.39   6089.44      1.00\n",
      "       z[42]      0.23      0.57      0.22     -0.68      1.18   4860.30      1.00\n",
      "       z[43]      0.57      0.65      0.55     -0.56      1.58   4518.07      1.00\n",
      "       z[44]      0.80      0.73      0.79     -0.36      2.00   4530.96      1.00\n",
      "       z[45]     -0.63      0.52     -0.62     -1.43      0.26   4988.77      1.00\n",
      "       z[46]      0.52      0.65      0.53     -0.65      1.52   4698.93      1.00\n",
      "       z[47]      0.24      0.65      0.25     -0.74      1.31   4951.08      1.00\n",
      "       z[48]     -0.14      0.65     -0.13     -1.16      0.95   4833.01      1.00\n",
      "       z[49]      0.73      0.44      0.74     -0.05      1.44   5569.92      1.00\n",
      "       z[50]     -0.03      1.03     -0.02     -1.83      1.59   4288.44      1.00\n",
      "       z[51]      0.06      1.02      0.04     -1.81      1.61   3672.90      1.00\n",
      "       z[52]      0.18      0.58      0.19     -0.77      1.14   5045.43      1.00\n",
      "       z[53]     -0.40      0.72     -0.39     -1.58      0.73   4013.68      1.00\n",
      "       z[54]      0.38      0.64      0.38     -0.72      1.37   4247.74      1.00\n",
      "       z[55]      0.39      0.53      0.40     -0.48      1.23   4775.47      1.00\n",
      "       z[56]     -0.05      0.68     -0.05     -1.09      1.13   4628.18      1.00\n",
      "       z[57]     -0.06      0.99     -0.06     -1.59      1.55   3953.52      1.00\n",
      "       z[58]      0.22      0.67      0.23     -0.96      1.28   4811.46      1.00\n",
      "       z[59]      0.16      0.64      0.17     -0.88      1.16   4578.49      1.00\n",
      "       z[60]      0.20      0.64      0.19     -0.76      1.37   6021.70      1.00\n",
      "       z[61]     -0.75      0.71     -0.74     -1.90      0.42   4696.80      1.00\n",
      "       z[62]      0.68      0.63      0.69     -0.31      1.75   4234.79      1.00\n",
      "       z[63]      1.33      0.69      1.34      0.09      2.40   5546.23      1.00\n",
      "       z[64]     -0.13      0.61     -0.13     -1.15      0.84   3691.09      1.00\n",
      "       z[65]     -0.02      1.00     -0.01     -1.77      1.47   5884.58      1.00\n",
      "       z[66]     -0.04      0.66     -0.05     -1.08      1.11   4222.86      1.00\n",
      "       z[67]     -0.05      0.66     -0.06     -1.05      1.11   4443.65      1.00\n",
      "       z[68]      1.11      0.53      1.11      0.28      2.06   5208.49      1.00\n",
      "       z[69]     -0.01      1.06     -0.01     -1.73      1.72   4987.85      1.00\n",
      "       z[70]      0.22      0.60      0.22     -0.74      1.18   4718.47      1.00\n",
      "       z[71]      1.00      0.68      1.01     -0.11      2.17   4243.02      1.00\n",
      "       z[72]      1.33      0.73      1.33      0.17      2.54   3875.87      1.00\n",
      "       z[73]     -0.10      0.52     -0.10     -0.95      0.76   4041.69      1.00\n",
      "       z[74]     -0.12      0.61     -0.13     -1.14      0.86   4663.50      1.00\n",
      "       z[75]     -0.06      1.01     -0.06     -1.51      1.84   4542.51      1.00\n",
      "       z[76]     -0.24      0.73     -0.26     -1.41      0.92   5198.86      1.00\n",
      "       z[77]     -0.35      0.67     -0.34     -1.48      0.73   6394.48      1.00\n",
      "       z[78]     -1.79      0.37     -1.80     -2.36     -1.14   5299.21      1.00\n",
      "       z[79]      0.66      0.67      0.67     -0.43      1.71   4307.13      1.00\n",
      "       z[80]      0.01      0.70      0.02     -1.09      1.19   4646.61      1.00\n",
      "       z[81]     -2.00      0.51     -2.01     -2.83     -1.16   4778.11      1.00\n",
      "       z[82]     -1.11      0.66     -1.11     -2.16     -0.02   5098.75      1.00\n",
      "       z[83]     -0.04      0.99     -0.05     -1.58      1.71   6808.99      1.00\n",
      "       z[84]      0.21      0.68      0.23     -0.86      1.32   4177.90      1.00\n",
      "       z[85]     -0.58      0.66     -0.58     -1.79      0.38   4588.05      1.00\n",
      "       z[86]      0.55      0.49      0.55     -0.29      1.30   4986.72      1.00\n",
      "       z[87]      0.13      0.40      0.13     -0.50      0.80   4056.14      1.00\n",
      "       z[88]     -1.00      0.55     -1.00     -1.84     -0.08   4706.97      1.00\n",
      "       z[89]     -0.97      0.61     -0.95     -1.91      0.05   4537.31      1.00\n",
      "       z[90]     -0.42      0.63     -0.41     -1.45      0.62   5595.05      1.00\n",
      "       z[91]     -0.27      0.65     -0.26     -1.36      0.76   5571.39      1.00\n",
      "       z[92]     -0.23      0.67     -0.23     -1.39      0.81   4150.08      1.00\n",
      "       z[93]     -0.39      0.70     -0.37     -1.48      0.79   6338.27      1.00\n",
      "       z[94]     -1.35      0.65     -1.37     -2.38     -0.29   4463.94      1.00\n",
      "       z[95]      0.48      0.68      0.47     -0.69      1.56   3927.82      1.00\n",
      "       z[96]     -0.12      0.62     -0.12     -1.06      0.96   4575.61      1.00\n",
      "       z[97]      0.24      0.63      0.23     -0.77      1.25   4992.10      1.00\n",
      "       z[98]     -0.16      0.66     -0.17     -1.15      0.96   4749.74      1.00\n",
      "       z[99]      0.29      0.44      0.30     -0.52      0.97   3934.25      1.00\n",
      "      z[100]      0.01      0.98      0.00     -1.77      1.42   4741.75      1.00\n",
      "      z[101]      1.05      0.61      1.05      0.08      2.08   4564.23      1.00\n",
      "      z[102]     -0.44      0.56     -0.44     -1.31      0.51   4224.95      1.00\n",
      "      z[103]     -0.08      0.63     -0.08     -1.17      0.88   5087.00      1.00\n",
      "      z[104]     -0.20      0.66     -0.19     -1.32      0.84   4488.40      1.00\n",
      "      z[105]     -1.25      0.72     -1.25     -2.41     -0.01   5090.42      1.00\n",
      "      z[106]      1.25      0.64      1.24      0.25      2.31   3537.05      1.00\n",
      "      z[107]      0.05      0.71      0.05     -1.15      1.17   6323.28      1.00\n",
      "      z[108]      0.24      0.66      0.24     -0.86      1.33   4763.78      1.00\n",
      "      z[109]      0.16      0.72      0.17     -1.03      1.31   7480.28      1.00\n",
      "      z[110]     -0.16      0.65     -0.17     -1.27      0.89   4656.33      1.00\n",
      "      z[111]     -0.44      0.71     -0.47     -1.49      0.86   4047.24      1.00\n",
      "      z[112]     -0.27      0.64     -0.27     -1.37      0.71   4326.19      1.00\n",
      "      z[113]     -0.27      0.44     -0.28     -0.94      0.49   4213.19      1.00\n",
      "      z[114]     -0.46      0.66     -0.45     -1.55      0.64   5152.98      1.00\n",
      "      z[115]      0.62      0.73      0.63     -0.67      1.68   5120.52      1.00\n",
      "      z[116]      0.82      0.64      0.81     -0.16      1.91   4596.87      1.00\n",
      "      z[117]     -0.94      0.72     -0.95     -2.06      0.31   4472.47      1.00\n",
      "      z[118]     -0.48      0.59     -0.49     -1.50      0.45   5269.26      1.00\n",
      "      z[119]      0.77      0.50      0.78     -0.06      1.54   4402.55      1.00\n",
      "      z[120]      1.02      0.65      1.03     -0.09      2.04   5745.43      1.00\n",
      "      z[121]      0.62      0.64      0.63     -0.49      1.62   6269.87      1.00\n",
      "      z[122]      0.18      0.75      0.20     -0.97      1.40   4402.07      1.00\n",
      "      z[123]      1.86      0.55      1.87      1.03      2.87   4658.53      1.00\n",
      "      z[124]      1.18      0.64      1.18      0.17      2.25   6082.30      1.00\n",
      "      z[125]      1.12      0.57      1.13      0.24      2.11   3867.44      1.00\n",
      "      z[126]     -0.01      0.98     -0.03     -1.67      1.53   4640.49      1.00\n",
      "      z[127]     -1.44      0.64     -1.45     -2.47     -0.36   4396.85      1.00\n",
      "      z[128]      1.17      0.63      1.16      0.15      2.19   4299.97      1.00\n",
      "      z[129]      0.95      0.43      0.96      0.25      1.66   4663.92      1.00\n",
      "\n",
      "Number of divergences: 0\n"
     ]
    }
   ],
   "source": [
    "# inference\n",
    "start = time.time()\n",
    "init_strategy = init_to_median(num_samples=10)\n",
    "kernel = NUTS(VAE_model, init_strategy=init_strategy)\n",
    "mcmc = MCMC(kernel, num_warmup=1000, num_samples=2000)\n",
    "rng_key, rng_key_infer = random.split(rng_key)\n",
    "mcmc.run(rng_key_infer, args, y=y_data)\n",
    "mcmc_samples = mcmc.get_samples()\n",
    "mcmc.print_summary(exclude_deterministic=False)\n",
    "t_elapsed = time.time() - start"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "996bc828",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MCMC elapsed time: 7 s\n",
      "Average ESS for all CAR effects : 4769\n"
     ]
    }
   ],
   "source": [
    "print(\"\\nMCMC elapsed time:\", round(t_elapsed), \"s\")\n",
    "ss = numpyro.diagnostics.summary(mcmc.get_samples(group_by_chain=True))\n",
    "r = np.mean(ss['vae_car']['n_eff'])\n",
    "print(\"Average ESS for all CAR effects : \" + str(round(r)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "a1985e30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['noise', 'vae_car', 'z'])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mcmc_samples.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "09da388b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# posterior predictive\n",
    "rng_key, rng_key_ = random.split(rng_key)\n",
    "posterior_predictive = Predictive(VAE_model, mcmc_samples)\n",
    "posterior_predictions = posterior_predictive(rng_key_, args)\n",
    "post_obs = posterior_predictions['vae_car']\n",
    "mean_post_pred_vae = np.mean(post_obs, axis=0)\n",
    "hpdi_post_pred_vae = hpdi(post_obs, 0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "75871e98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABAYAAADtCAYAAAAslneLAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAA26klEQVR4nO3de5xkZX3v+++3e3ruAzPDcJ3h5mZkixrBjKjbmOARFfBCtpcEkqAx+4RjEqLmmGOM7hPd7p29fZ3sGGM0mtleiRe8ohhRwAtBsyNyERQYwBG5DMNtGJgLc+3u3/mj1piiqequXk9VrfWs/rznVa/pqlq/ep6qrv7W008/ay1HhAAAAAAAwNw0UnUHAAAAAABAdZgYAAAAAABgDmNiAAAAAACAOYyJAQAAAAAA5jAmBgAAAAAAmMOYGAAAAAAAYA6bV3UHAOTrJS9YEg9vnehp2+t+vPeyiDhjwF0CgDmFHAaA6jUhi5kYAFDalq0TuvqyNT1tO3bkz1YNuDsAMOeQwwBQvSZkMRMDAEoLhfZHb7OjAID+I4cBoHpNyGKOMQAgyWSP/6Zj+2jb37W9wfbNtt/UYRvbfr/tjbZ/bPuZA3tSAJCRfuSwRBYDQIrcx8SsGABQWig0EdGPhxqX9JaIuN72MknX2b4iIm5p2+ZMSWuLy7Mlfaj4HwDmrD7msEQWA0ApTRgTs2IAQJJJRU+X6UTEfRFxffH1DkkbJK2estnZki6Mlh9IWm77yEE8JwDIST9yWCKLASBF7mNiVgwAKC0kTfQw2Cyssn1t2/X1EbF+6ka2j5N0iqSrp9y1WtI9bdc3Fbfd12sHAKBpBpHDElkMALPRhDExEwMAkvTyV6jClohYN90GtpdK+pKkN0fE9ql3dyjp2/pZAMhVP3NYIosBoIzcx8RMDAAoLSTt79O+rbbH1ArAT0fElztssknS0W3X10ja3JfGASBT/cxhiSwGgDKaMCbmGAMASguFJnq8TMe2JX1U0oaIeG+XzS6R9NriSKzPkbQtIli6CmBO61cOS2QxAJTVhDExKwYAlBfSRH8mR58n6TxJP7F9Q3Hb2yUdI0kR8WFJl0o6S9JGSbskvb4vLQNAzvqXwxJZDADlNGBMzMQAgNJC6uHM2D08TsT31Xl/qfZtQtIf9aE5AGiMfuWwRBYDQFlNGBMzMQAggTUxfXYBAAaKHAaA6uWfxUwMACitdaCVvEMQAHJGDgNA9ZqQxRx8sM9sf8L2fxtiey+2/ZUhtHOn7dMH3U5Ztj9s+/9NfIw32n5Pv/o0F7TO2eqeLgAGz/aVtv/PqvuB4SGHgfqw/Xzbt1XdDwxfE7KYiYEK9WkA998l/eKXWdth+4TEfg11cqMfIuINEfFfEx9mvaTfsX1YP/o0V0yGe7oAeLzUCVfb77L9qX72CXkih9E0ti+z/e4Ot59t+37b84rrpxVj37dO2e644vadUy6/2ed+Pm7cHRHfi4gT+9lGW1vZjc/nmtyzmImBjNl+lqSDI+IHs6gZ+u4jtvt3vOQBiog9kr4h6bVV9yUXTZgdBeqoiqxGnshhNNQnJJ1XnLqt3Xlqndt9vLj+Oklbi/87WR4RS9sunxtMdzHXNSGLmRhIZPsU29fb3mH7c5IWtt23wvY/2X7I9iPF12uK+/5S0vMlfaCYwfxAcfvf2r7H9nbb19l+/jTNnynpn9vau6r48sYDs6LFTOom239m+35JH7f9u7a/P+V5hO0TbJ8v6bclvbV4jK+1bXay7R/b3mb7c7YXqo+Kv3593vaFxet5s+11bfc/pVhl8Whx3yva7vvFLKrtVcVr/ajtrba/Z3ukuO8o218qvic/t/3GKd24UtJL+/m8mixkTWikpwuAf2P7H9U69dDXiqx9a5HD/8n23ZK+cyC/p9Tdaft022eodfqi3yzqb2zb7Fjb/1Lk6OW2Vw3vmWHYyGE01FckrVRrrCypNa6W9DJJFxbXF0t6tVpHZ1/bPmacLdsH2/6o7fts32v7v9keLe47wfY/F+PfLcV4f9pxd9vj3mn7/ynGz48VbRxu+xtFRn+reF4Htv+CWysittm+yvZTi9s7js97GNdiSJqQxfXtWQZsz1cruP5RrfD6gqRXtW0yIunjko5VawC4W9IHJCki3iHpe5IuKGYwLyhqrpF0cvF4n5H0hWl+AX+6pF/sxxQRv1p8+Ywps6JHFI93rKTzp3tOEbFe0qcl/X/FY7y87e7fkHSGpOMl/ZKk353usUp6haSLJC2XdImK18v2mKSvSbpc0mGS/ljSp213Wq71FkmbJB0q6XC1Bs9RTA58TdKNklZLeqGkN9t+SVvtBknP6PuzarDcl00BVYiI8yTdLenlEbFU0ueLu35N0lMkvaRbbVH/TbV2JftckdXtufVbap3T+DBJ8yX9aZ+7j5ohh9E0EbFbrVxsX8X5G5JujYgDE6GvkrRTrfH3ZUpb8flJSeOSTpB0iqQXSzqwu+9/VWv8uULSGkl/V/Sx27h7qldJepGkJ0t6uVqrU98uaZVavyu0/zL/DUlr1crv69Uak3ccn/c4rsUQ5Z7FTAykeY6kMUnvi4j9EfFFtX6xlyRFxMMR8aWI2BUROyT9pVqDvq4i4lNF3XhE/LWkBZK67au0XNKOHvo5KemdEbG3CNqy3h8RmyNiq1pBdHLCY3Xz/Yi4NCIm1JpwOTDYfY6kpZLeExH7IuI7kv5J0rkdHmO/pCMlHVt8X75XnO/zWZIOjYh3F49xh6T/Jemcttodkg4ewPNqpJC1L0Z7ugDoybsi4rHErP54RNzeNrA+uT9dQx2Rw2iwT0p6je1FxfXXFrcd8Dq1Jkcn1Ppj2rnFH5LabSlWkB64PGVqI7YPV2sV7puL/H1Q0t/o38aH+9X649pREbGnOM/8bPxdRDwQEfeq9UfBqyPiRxGxV9LFak1ESJIi4mMRsaO4712SnmG727i0l3EthqQJWczEQJqjJN1b/NJ5wF0HvrC92PY/2L7L9nZJV0lafmBpUie232J7Q7GE6FG1fknttgz0EUnLeujnQ8X+86nub/t6l1q/qD+B7V9pD+HitvZQ/pVZtLHQrX1tj5J0T0RMtt1/l1ozpFP9laSNki63fYfttxW3HyvpqCl9e7taqwoOWCZp2zT9Q5uQNKmRni4AenJPHx6jp6xGM5DDaKriF/CHJJ1t+0lq/SL8GUmyfbSkF6j4i7qkr6q1O+/U3UFXRcTytsuGDk0dq9Yf+u5rGx/+g1p/tZekt0qypB8Wu7L+3iyfygNtX+/ucH1p8ZxGbb/H9s+K3xvuPPAcujxuL+NaDEkTspiDG6W5T9Jq226bHDhG0s+Kr9+i1l/7nx0R99s+WdKPpF8cdeJxB+Vz63gCf6bWUqCbI2LS9iNt20/1Y7WWJc1k6sH/HpO0uK3dI2bYflaKIF/e9vgREcu7FvRms6SjbY+0TQ4cI+n2Du3vUOu1f0uxb9Z3bV+j1oD75xGxdpp2nqLWkiz0qM4HUQFqrlPWtt82NatH1dpFarp6zEHkMBrsQrVWCpwo6fKIOPBL9Xlq/YHza/634xMuLLb9yizbuEfSXrUmEcan3hkR90v6fan1xy9J37J9VURsnGU7M/ktSWdLOl2tSYGD1fojYMffG9TbuBZDlHsW13fKIg//qtb+SG+0Pc/2KyWd2nb/MrVmAh+1vVLSO6fUPyDpSVO2H1drdnSe7b+QdNA07V+qJ+6aMPUxO7lR0lNtn1wcv+BdJR5j2K5Wa5D8Vttjtk9Taz+ti6ZuaPtlxYFiLGm7pIni8kNJ2906EOOiYmb2aW6d3eGAX1Nr/y70IMKaiJGeLgCeYKasvV2tVVMvLZbH/me1di9rrz+u2M8UcxQ5jIa7UK1flH9fj9+N4LWS/otau0oduLxK0kttHzKbBiLiPrWOIfDXtg+yPWL739n+NUmy/RoXBw9X6xf11gHoW/o5Zl6m1gTFw2pNCv/3KfdPbauXcS2GpAlZXN+eZSAi9kl6pVoH4XtE0m9K+nLbJu+TtEjSFkk/kPTNKQ/xt5Je7dYZC96v1oFTvqHWYPAuSXs0zbLSiLhe0jbbz267+V2SPlksKfqNLnW3S3q3pG9J+qmkqftKfVTSScVjfKVb+8NUvNavUGsfsC2S/l7SayPi1g6br1Xrue1Ua/Lm7yPiymIftJer9eHx8+JxPqLimALFJMlZevwHD2YwKfd0AfAE/0PSfy6Wf7566p0RsU3SH6qVU/eqNTnafpaCLxT/P2z7+sF2FXVGDqOpIuJOSf9b0hK1Dkot28+RdJykD0bE/W2XS9TalbT9+FOPFkfxP3D5v7s09Vq1DtZ6i1pj+i+qdbwqqbULw9W2dxZ9eFNE/Ly4712aYdw9CxeqNf6/t+jH1NORP258PtO4FsOXexb78bvHIze2XyzpDyPi16vuS+5s/7GkoyPirVX3JRdrn7443vvVE3ra9hX/7ifXRUTpUwkBAJ6IHAaA6jUhiznGQOYi4nK1lj8hUUT8XdV9yM2BA60AAKpBDgNA9ZqQxUwMAEgyUePzsQLAXEAOA0D1cs9iJgYAlBayJjKfHQWAnJHDAFC9JmQxEwMAkkzW+OiqADAXkMMAUL3cszjv3gOoVOt8PSM9XWZi+2O2H7R9U5f7T7O9zfYNxeUv+v18ACA35DAAVK8JWTyQFQOjS5bE2IqV5R8g8UQJo3vL13oirfH9S9P2LZm3cDypftG8/Un1O7cvKl0bo0lNa2xnWn3qJN3kWGL9wvLvnXljEzNvNJ2t5X+U9+7cqvE9j5V644as/anf+H/zCUkfUOt0Pd18LyJe1q8Gm2x02ZKYt2pF6fp5O9KybDLh02XensQcXpzW91g4mVQ/MpLW/8nxhDCbSHvuI2kfIcmfA0576ZPqY1liDj9W/snv37ZV47vI4SYaXbIk5iWMiZ04Jk79mU4xsSCt3vPTAmF0JK1+fE91C6tH9yQ+QOKYOHlMnTAmTjWyq/zn4P7tWzW+e+5m8UDe8WMrVmrNG/+kdL0TQ+ygO8rXLnokbWBw76+m/SQdcuLDSfVPPeT+pPp/vfxppWv3L0sLgSO/n/rLQNprv/PotAH17hPLp/jhh21LanvyM4eVrr3l639TujZCmujTsqmIuMr2cX15MGjeqhU68r9cULr+kH+en9T+vuXlf56Wb0ybIH3o5LSPtr0n7k6qX7I0bUS346GlpWtHdqQNSpbcm/bzvHd5Wo7P252WwykTzBMveDSp7clrlpeuvfOj7y1dSw7X27wVK7XmTeXHxKN70n4mFt+f8DOZ+Lvd9hMS8+CYx5LqD1qSlsVbNxxSutaTad+3g29LKtd44gT5/vIfQ5KkXU8u/1daJ06uL7t+YenajZ+Z21nMrgQAEliTPV765Lm2b7T9DdtP7deDAkC+yGEAqF7+WczBBwGUFprV7Ogq29e2XV8fEetn0dz1ko6NiJ22z5L0FUlrZ1EPAI1DDgNA9ZqQxUwMAEgyi1OzbImIdWXbiYjtbV9favvvba+KiC1lHxMAmoAcBoDq5Z7FTAwAKC1kTUbflkRNy/YRkh6IiLB9qlq7QqUdlAMAMkcOA0D1mpDFTAwAKC0k7Y/+xIjtz0o6Ta3lVZskvVPSmCRFxIclvVrSH9gel7Rb0jkRUd1hbwGgBshhAKheE7KYiQEACayJPh1EJSLOneH+D6h16hYAwC+QwwBQvfyzmIkBAKWFpMk+nZoFADB75DAAVK8JWczEAIAk/ZodBQCUQw4DQPVyz2ImBgCUFuHsZ0cBIGfkMABUrwlZzMQAgNJaB1oZrbobADBnkcMAUL0mZDETAwASWBOZz44CQN7IYQCoXv5ZzMQAgNJaB1rJe38qAMgZOQwA1WtCFjMxACDJhPKeHQWA3JHDAFC93LN4IBMDMS+0f9X+0vVHfDuxWwmTNfe+qny/JSm2z0+qf3jr0qT6K+95SlK9DpsoXbr8yO1JTe+4e2VS/fa140n1h/4wbb+gY190f+na2244JqntpYeUf9NPJjztkLOfHW2sSSn2lP/m7joi7fvqyfK1W56e9hmwf2kk1c+7a2FS/Z6RtPol28q/9ruesiep7dic1vfxJWmv/ejetPfdtlP2li/eujip7fmLyj/3lNWn5HDNjYbGDy4/tlp6T2IeLiv/3tizMu3neWJJwgeBpIkdC5LqH3o0Lc+8MOH5L9uX1PaOvWnPvfX36/JG9yVmSkom7Ux7z0+mvHRzPItZMQAgyWTms6MAkDtyGACql3sWMzEAoLQIaf9k3iEIADkjhwGgek3IYiYGAJTWWjaVdwgCQM7IYQCoXhOymIkBAEkmUg7qAQBIRg4DQPVyz+KepjVs/4ntm23fZPuzttOO5gGgEQ6cmqWXC9KQwwA6IYeHiywG0EkTsnjGiQHbqyW9UdK6iHiapFFJ5wy6YwBy0Fo21csF5ZHDALojh4eFLAbQXf5Z3OuuBPMkLbK9X9JiSZsH1yUAOZnMfNlURshhAB2Rw0NFFgPoKPcsnnFiICLutf0/Jd0tabekyyPi8qnb2T5f0vmSNHrI8j53E0AdtY7AOlp1NxqvVA6vXD7UPgKoBjk8PGQxgG6akMW97EqwQtLZko6XdJSkJbZ/Z+p2EbE+ItZFxLrRpUv631MAtdM6Amve+1PlgBwG0A05PDxkMYBumpDFvezkcLqkn0fEQxGxX9KXJf2HwXYLQC4m5Z4uM7H9MdsP2r6py/22/X7bG23/2PYz+/5k6oscBtAVOTw0ZDGArnLP4l4mBu6W9Bzbi21b0gslbehH4wDy1ucjsH5C0hnT3H+mpLXF5XxJH0rtf0bIYQAdkcNDRRYD6KgJWTzjxEBEXC3pi5Kul/STomZ9PxoHkL9+HYE1Iq6StHWaTc6WdGG0/EDScttH9ulp1Bo5DGA65PBwkMUAppN7Fvd0VoKIeKekd6Y2BqBZIqzx4Z12ZbWke9qubypuu29YHagSOQygE3J4uMhiAJ00IYt7PV0hAHQ0i4OorLJ9bdv19RExm7+0dGooZlEPAI1EDgNA9XLPYiYGAJR2YH+qHm2JiHUJzW2SdHTb9TXi/NEA5jhyGACq14QsHsjEwDHLHtZ7T/tU6fq33/x7Se3vPHaydO1h31iQ1vZrtifV792b9i2J/fOT6hc8VP78m9v2Lk9q+8iX3J9Uv+faw5Pq9y1LO33Iz688rnTt6MK0Sb6Dzyy/cmj0n/YntT3E065cIukC2xdJerakbRExZ5avztZBS3brxc/8Sen67249Oan9kRN2lq49+J+WJrW9/ZTybUvSvj2JH42JPxJ75pf/HIrH0vr+2DETSfVL70o7h/PonqRy7Ul47Rffnvb5ecwZd5auffDCfUltk8P1tWjRPp1y0s9L19/ywNqk9icXlB9fzNuV9r4aX55UrvlL034uxjcvTqpPef77lqS9dvtXlP9dRpJG9qa1v+CRtPp5D46Vro15aWPivc8sPwaIL6S97rlnMSsGAJR24Jyt/WD7s5JOU2t51Sa19uEck6SI+LCkSyWdJWmjpF2SXt+XhgEgY+QwAFSvCVnMxACAJL2cj7UXEXHuDPeHpD/qS2MA0CDkMABUL/csZmIAQGkR0vjk0I7ACgCYghwGgOo1IYuZGACQZIj7UwEAOiCHAaB6uWcxEwMASuvn/lQAgNkjhwGgek3IYiYGACSJzEMQAHJHDgNA9XLPYiYGACTp14FWAADlkMMAUL3cs5iJAQClReS/PxUA5IwcBoDqNSGLmRgAkMCayPwIrACQN3IYAKqXfxYzMQAgSe77UwFA7shhAKhe7lnMxACA0kL5L5sCgJyRwwBQvSZkMRMDAMqL1j5VAICKkMMAUL0GZDETAwCS5H4EVgDIHTkMANXLPYuZGABQWjTgQCsAkDNyGACq14QsHsjEwOb7Vuldf/n60vUHn3NfUvtPX/ZI6dp/WfDkpLYP/erBSfUrzr0/qX7Tw4uS6vccu6907eFHPprU9qNXHZFUv3xT2vqdnauTyrX3SXvSHiDBRIX7NOW+bKqpdm5drP/9hVNK1y/5la1J7R950PbStT89aWlS25P3LkmqX3j0jqT6BWPjSfWPbB8r3/ZDaR/r+5dNJtU77alr78q0+pQ8euz4tM5v2lb+83/fxGhS2+Rwfe3ZvkAbvr22dP2+xLHF047bXLr2tu8fn9T2wvvS8mjvosRfU1aWH9NK0r6DEn7J25v2Mz1vR9ovmPMfTRsXeiKpXOMrE/J0PK3v80aqC8Tcs5gVAwCS5H4EVgDIHTkMANXLPYuZGABQWkT+IQgAOSOHAaB6TchiJgYAJMn91CwAkDtyGACql3sWMzEAIEnu+1MBQO7IYQCoXu5Z3NORLWwvt/1F27fa3mD7uYPuGID6C1mTkyM9XZCGHAbQCTk8XGQxgE6akMW99uxvJX0zIv69pGdI2jC4LgHISfR4mYntM2zfZnuj7bd1uP8029ts31Bc/qJ/zyIL5DCAjvqVwxJZ3AOyGEBHuY+JZ9yVwPZBkn5V0u9KUkTsk5R2/g8AzdCnA63YHpX0QUkvkrRJ0jW2L4mIW6Zs+r2IeFlyg5khhwF01ccDXpHF0yOLAXTVgDFxLysGniTpIUkft/0j2x+xnXaSaADN0Z/p0VMlbYyIO4qB1kWSzh5Qj3NEDgPorn9LBsji6ZHFALrLfEzcy8TAPEnPlPShiDhF0mOSOi1pON/2tbavHd/zWJ+7CaCuItzTRdKqAxlRXM5ve5jVku5pu76puG2q59q+0fY3bD91gE+rbmadwxO7yWFgruhTDktk8Uxmn8W7yGJgrsh9TNzLWQk2SdoUEVcX17+oDiEYEeslrZekJauOzvyYjAB6EZImJ3teNrUlItZ1ua/Tg0zNkeslHRsRO22fJekrktb22njmZp3Di44gh4G5oI85LJHFM5l1Fi88iiwG5oImjIlnXDEQEfdLusf2icVNL5Q0dR8HAHNRSAr3dpneJklHt11fI2nz45qK2B4RO4uvL5U0ZntVH59NbZHDALrqXw5LZPG0yGIAXTVgTNzLigFJ+mNJn7Y9X9Idkl6f2jCAZujTOVuvkbTW9vGS7pV0jqTfat/A9hGSHoiIsH2qWhObD/el9TyQwwA66uO5s8nimZHFADrKfUzc08RARNwgabqlZwDmqj6EYESM275A0mWSRiV9LCJutv2G4v4PS3q1pD+wPS5pt6RzIvo4HK45chhAV31KQrJ4ZmQxgK4yHxP3umIAADr4xUFUkhVLoS6dctuH277+gKQP9KUxAGiM/uWwRBYDQDn5j4mZGACQZs78nQgAaoocBoDqZZ7Fg5kYWDEuvar8bg733HFoUvNXnX1x6dpf+tJJSW3vTzyb7ZpFO5Pqjzp5W1L9rvH5pWs3/+PxSW3rsLTyh9ZNJtWvvjKt/XufklC8bSyp7R03HlG6dmJ7QtshRe9HYMUQxZJJ7f3l8nmy57GFSe0/67iflK792cSxSW0vuaOXM/F298Lnb0iq/86mJyfVj63YW772zrSPdUfaazd52qNJ9fO/szyp3j9dULp294l7ktree9Py0rWxe7R8w+RwrcWC0J7jyv9MzxtLG9uMT5b/mR5fnPZbzkjC21qSFi7Zl1S/aEFa/SNbl5aunfdQ2rhuZH9SuZz2tunthPbTtb+n/APM25XW+MjmZeWLdye03YAsZsUAgER5hyAA5I8cBoDq5Z3FTAwASJP5sikAyB45DADVyzyLmRgAkCbzEASA7JHDAFC9zLOYiQEA5YWkPh4NGwAwS+QwAFSvAVnMxACAJHPn7NUAUE/kMABUL/csZmIAQJrMj8AKANkjhwGgeplnMRMDAJI489lRAMgdOQwA1cs9i5kYAFBeKPsDrQBA1shhAKheA7KYiQEACZz9gVYAIG/kMABUL/8sZmIAQJrMZ0cBIHvkMABUL/MsZmIAQJrJqjsAAHMcOQwA1cs8i5kYAFBeA87ZCgBZI4cBoHoNyGImBgAkyf0IrACQO3IYAKqXexYzMQAgTeYhCADZI4cBoHqZZ/FI1R0AAAAAAADVGcyKga3zNPrZlaXLDz4kbb7i+NHfL1276Lnbk9r+Hyd/Man+gm+fl1S/cOWepPqDv7qkdO3Ybz+Y1vbY/qT6HZ9anVQ/MZY2zbfyewtK1y7dNJ7U9kOnjJYvTtwdql/LpmyfIelvJY1K+khEvGfK/S7uP0vSLkm/GxHX96f15hnbYq3++PzS9Xefmfbx8KnJU0vXjiR+Mv3Kedcl1V9yxbOT6icWpf1QHPn98vUPvWpnUtujo2l9X3bRQUn1MZp25Kb9yxLGD9vGktoeX1z+tYvEP9P0c/kqWdxfo49Zy68tPz4YX5TW/h2nHlK6NlbuS2p70cG7k+oXzJtIqt+6sfzvIpI0b1f5AVIkDMskaeKEtNdu5JbFSfVLNqdl8YKt5UNtsvzQRZK0L+FjyIkHD8x9TMyKAQDlhaRJ93aZhu1RSR+UdKakkySda/ukKZudKWltcTlf0of6/nwAIDd9ymGJLAaA0howJmZiAECa6PEyvVMlbYyIOyJin6SLJJ09ZZuzJV0YLT+QtNz2kf16GgCQrf7ksEQWA0B5mY+JmRgAkMTR22UGqyXd03Z9U3HbbLcBgDmnTzkskcUAUFruY2LOSgAgTe/7U62yfW3b9fURsb74utO6qqmP3Ms2ADD39CeHJbIYAMrLfEzc88RAsb/DtZLujYiXpTYMoCF6j6EtEbGuy32bJB3ddn2NpM0ltmk0chhAR/3JYYks7glZDKCjzMfEs9mV4E2SNqQ2CKA5el0y1cOyqWskrbV9vO35ks6RdMmUbS6R9Fq3PEfStoi4r+9Pqt7IYQCP08cclsjiXpHFAB6nCWPiniYGbK+R9FJJH0ltEEDD9OEIrBExLukCSZepNdj6fETcbPsNtt9QbHappDskbZT0vyT94eCeVP2QwwC66tNZCcjimZHFALrKfEzc664E75P0VknLum1g+3y1Tpeg+UtWJHcMQB76dc7WiLhUraBrv+3DbV+HpD/qT2tZep9mkcMLFi4fSqcAVK9fOSyRxT14n2aRxWNLGRMDc0XuY+IZVwzYfpmkByPiuum2i4j1EbEuItbNW7Ckbx0EUHP9O00WuiiTw2PzyWFgziCHh6LUmHgRWQzMGZlncS8rBp4n6RW2z5K0UNJBtj8VEb8z2K4BqL3e91tFGnIYQGfk8DCRxQA6a0AWz7hiICL+PCLWRMRxah384DsEIIBfyHx2NAfkMIBpkcNDQRYDmFbmWdzz6QoBoBNPVt0DAJjbyGEAqF7uWTyriYGIuFLSlQPpCQBgRuQwAFSPLAbQNKwYAJCmxkuiAGBOIIcBoHqZZzETAwDKa8CBVgAga+QwAFSvAVk8kImB0f2hpZv3la5/5KQFSe0vP3xH6dr41sqktv/k9tcn1b/8xdcm1d/yp09Pqt9zSPl39EHnPZrU9m3vOyapfsVoUrmW3/RIUv2+w8qfkmjfQWk/igfdWX6nppHyP6otmYdgU3kiNH9b+W/u4s3zk9p/bKx8/fiq/UltX/mlX06qn/+sbUn1Cy8/KKn+wXUuXXvI1xYntb1/afm2JWn3oWn1h/2w/Oe3JI3uLf/8JxbOeDzmacWJj5Wu9fzEHVPJ4drypDR/e/lv0N4VaT9Tex9dWLp24b1jSW3vOC6t77sWTCTVH3R72s/0gm3lfy4n5qc990djUVL9srvTQmHenrT60X0Jr92CtNdudE/57/vIeFLT2WcxKwYApMk8BAEge+QwAFQv8yxmYgBAaVb+R2AFgJyRwwBQvSZkMRMDAMprwP5UAJA1chgAqteALGZiAECazEMQALJHDgNA9TLPYiYGAKTJPAQBIHvkMABUL/MsZmIAQJLcl00BQO7IYQCoXu5ZzMQAgDSZhyAAZI8cBoDqZZ7FTAwAKC/yPwIrAGSNHAaA6jUgi5kYAJAm89lRAMgeOQwA1cs8i5kYAJBkGPtT2V4p6XOSjpN0p6TfiIhHOmx3p6QdkiYkjUfEusH3DgCqRQ4DQPVyz+KRfnYUwBwUPV7SvE3StyNiraRvF9e7eUFEnMxgFMCcQQ4DQPUyz2ImBgCU12sApofg2ZI+WXz9SUm/nvyIANAE5DAAVK8BWczEAIDSrNayqV4uiQ6PiPskqfj/sC7bhaTLbV9n+/zkVgGg5shhAKheE7KYYwwASDKLgFtl+9q26+sjYv0vHsf+lqQjOtS9YxbdeV5EbLZ9mKQrbN8aEVfNoh4AskMOA0D1cs9iJgYApOk9BLdMt49TRJze7T7bD9g+MiLus32kpAe7PMbm4v8HbV8s6VRJDEgBNBs5DADVyzyLBzIxML7Q2nrigtL1B21Ma3/LqmWlaxeuSGv7hOfelVT/zKVp9d88I+04P/tXjJeu3XrSiUltr7gybW3N4V+/I6l+YvWqpPr5t2wqXTv6QMef6Z4teP4p5dvel3jS1eGcmuUSSa+T9J7i/69O3cD2EkkjEbGj+PrFkt49lN7V0L6DRnT3S5aWro/EHc1icfksOejH5T8/JGn+C7ck1R+5bHtS/e2rD0qq90T52l1HpH3jxhcnlevQH5X/vkvSvhVp3/t9y8o//+O/9GhS2/tXLCpd+8BDTmqbHK6vsDSxMOEBEt8a3pOQCYltjy3an1R/wuFpWX7ricck1Y/uLf8CLL4v7cVb8IRjzM/O0k17k+pjXlr/R3eV/ywY27orqe1dxx9cunZkPDFMM89ijjEAoLwe96Xqw/5U75H0Its/lfSi4rpsH2X70mKbwyV93/aNkn4o6esR8c3klgGgzshhAKheA7KYXQkApBnC7GhEPCzphR1u3yzprOLrOyQ9Y/C9AYCaIYcBoHqZZzETAwCSOHFPBABAGnIYAKqXexbPuCuB7aNtf9f2Bts3237TMDoGIA9DWjY1p5HDAKZDDg8HWQxgOrlncS8rBsYlvSUirre9TNJ1tq+IiFsG3DcAdRca1oFW5jpyGEBn5PAwkcUAOmtAFs+4YiAi7ouI64uvd0jaIGn1oDsGIBPR4wWlkcMApkUODwVZDGBamWfxrI4xYPs4SadIunogvQGQFaveS6KaiBwG0I4crgZZDKBdE7K454kB20slfUnSmyPiCSd5tn2+pPMlaWzpir51EEC9eTLzFMzIbHJ43sHkMDBXkMPDxZgYQCe5Z/GMuxJIku0xtQLw0xHx5U7bRMT6iFgXEevmLVrSzz4CqKtel0zlnZO1MNscHl1MDgNzAjk8VLMeEy8ki4E5oQFZPOOKAduW9FFJGyLivYPvEoCc5L5sKgfkMIDpkMPDQRYDmE7uWdzLioHnSTpP0v9h+4bictaA+wUgF5nPjmaCHAbQHTk8LGQxgO4yz+IZVwxExPfVOp4CADxB7rOjOSCHAUyHHB4OshjAdHLP4lmdlQAAniDzEASA7JHDAFC9zLOYiQEA5YXkyao7AQBzGDkMANVrQBYPZmIgpJGJ8uUPPzPtVV1811jp2tE9SU1r88XHJdX/zWha/YLE7+iCLeVfu8nypZKkPWc94Yw/szLxo1VJ9be/aUFS/ZKbTihde9CdT0pqe/728j9wMVJ+VWQTztnaVGM7Q0f+y97S9Xe9NPEHeu9o6dIdp6QF8fzr0rJgZ6TVjy9L+wwb3VX+Z3J8YVLT2v2k8u8ZSRr917T2tzwjLYcjYZH3Q6cuT2p712HlG993KzncVDEq7V1e/vs7mTium7ezpxOQdW57NO2NNf+GpUn1dzmtfmlanGkiIY52H5r22k3OT6vffuz8pPodx6XtMTOyv3z7K29N/BxIGNfO9TExKwYApInMUxAAckcOA0D1Ms9iJgYAJMl9dhQAckcOA0D1cs9iJgYAlFfz064AQOORwwBQvQZkMRMDAJLkfqAVAMgdOQwA1cs9i5kYAJAk9xAEgNyRwwBQvdyzuPyhSgEg1DrQSi+XBLZfY/tm25O2102z3Rm2b7O90fbbkhoFgByQwwBQvQZkMRMDAJI4erskuknSKyVd1bUf9qikD0o6U9JJks61fVJyywBQc+QwAFQv9yxmVwIAaYZwoJWI2CBJ9rTnlz1V0saIuKPY9iJJZ0u6ZeAdBIAqkcMAUL3Ms5gVAwBKs2Y1O7rK9rVtl/P73J3Vku5pu76puA0AGoscBoDqNSGLWTEAoLwIebLn6dEtETHdvlDfknREh7veERFf7eHxO02dZn7iGACYATkMANVrQBYzMQAgTZ+GfBFxeuJDbJJ0dNv1NZI2Jz4mANQfOQwA1cs8i9mVAECSIR1opRfXSFpr+3jb8yWdI+mSobQMABUihwGgerlnMRMDAMoLSZPR2yWB7f9oe5Ok50r6uu3LituPsn2pJEXEuKQLJF0maYOkz0fEzUkNA0DdkcMAUL0GZDG7EgBIM5wjsF4s6eIOt2+WdFbb9UslXTr4HgFAjZDDAFC9zLOYiQEASYa0JAoA0AU5DADVyz2LBzIxMDIhzd9e/pUZPWRvUvvPedbG0rW3PHJ4UtsL3r8yqT51546Y/pyWM5q/Y3/p2rtPX5jU9tMPfSCp/qZXPDmpfukNSeVafPqDpWv3f/7QpLZ3HD1Wunb8+rT3zCyOwIohmlhgbT9+fun6455+b1L7rzzqR6Vr/+eVZya1PbYjqVzzd6S9p5f8aDKpfsea8h/NO49N6/vz//1Pk+pvftJTk+rHFyeVa/ea8p9hy74zmtR2JHx+j4wnNU0O15gnpAVby39/dp60L6n9lavKB+Kj25YktX3wFWnjwtRfskbG0x4g5efy4aemDegXnvRoUv1jj6xIqvdEUrl2ryn/4u3cXt3frSfLD6cl5Z/FrBgAUF6IE1EBQJXIYQCoXgOymIkBAKVZkiPzFASAjJHDAFC9JmQxEwMA0qStmgYApCKHAaB6mWcxEwMAkuQ+OwoAuSOHAaB6uWdxT0fGsH2G7dtsb7T9tkF3CkAmYhYXJCGHAXREDg8VWQygowZk8YwrBmyPSvqgpBdJ2iTpGtuXRMQtg+4cgLqL7I/AmgNyGEB35PCwkMUAuss/i3tZMXCqpI0RcUdE7JN0kaSzB9stANmI6O2CFOQwgO7I4WEhiwF0l3kW9zIxsFrSPW3XNxW3PY7t821fa/va/Xsf61f/ANRZSJ7s7YIks87h8T3kMDAnkMPDRBYD6KwBWdzLxIA73PaEqY6IWB8R6yJi3diCJek9A5CHzGdHMzHrHJ63kBwG5gxyeFjIYgDdZZ7FvZyVYJOko9uur5G0eTDdAZCd+uZbk5DDALojh4eFLAbQXeZZ3MvEwDWS1to+XtK9ks6R9FsD7RWAbHiyxmuimoMcBtAVOTw0ZDGArnLP4hknBiJi3PYFki6TNCrpYxFx88B7BqD+QlLeGZgFchhAV+Tw0JDFALpqQBb3smJAEXGppEsH3BcAmbFCrvG+Uk1CDgPohBweLrIYQCdNyOKeJgYAoKvMQxAAskcOA0D1Ms9iJgYApMk8BAEge+QwAFQv8yweyMTAY49s2nL1RX96V5e7V0naMu0DXJTW/h1p5TP3rzp17pt0ZVr/NvaxKx0M/rX769KVVX9fjy1dOaT9qWy/RtK7JD1F0qkRcW2X7e6UtEPShKTxiFg3+N7V0+4tm7b8aP1buuWwNNP7bn1a+1cmVX+36p+JmdS5f0l9S/z8nEmdXzfdXW3/yOGG2r1l05YffaRrFs/8nvtIWvt3p5Un/Uzcmdb2TGqdJ6p3/+hbd3M6iwcyMRARh3a7z/a1df6QqHP/6tw3qd79o2+DM6QjsN4k6ZWS/qGHbV8QEXX9wBua6XJYqvf7rs59k+rdP/pWXt37Nx1yuL4YEw9Gnfsm1bt/9G1wcs9idiUAkCCGsmwqIjZIku2BtwUAeSGHAaB6+WfxSN8fEcDcEWqFYC8XaZXta9su5w+oR5fbvm5Ajw8A9UIOA0D1GpDFVawYSNxzdeDq3L86902qd//o26D0vmpqy3TLw2x/S9IRHe56R0R8tcc2nhcRm20fJukK27dGxFU993BuqfP7rs59k+rdP/pWXt371x05nKu6v+fq3L86902qd//o26BknsVDnxiIiFp/w+vcvzr3Tap3/+jb4PTrnK0RcXofHmNz8f+Dti+WdKokBqQd1Pl9V+e+SfXuH30rr+79mw45nKe6v+fq3L86902qd//o2+DknsXsSgAgTe/LpgbK9hLbyw58LenFah2gBQCajRwGgOplnsVMDAAoL0KamOztksD2f7S9SdJzJX3d9mXF7UfZvrTY7HBJ37d9o6QfSvp6RHwzqWEAqDtyGACq14AsHtjEgO0zbN9me6Ptt3W437bfX9z/Y9vPHFRfOrR9tO3v2t5g+2bbb+qwzWm2t9m+obj8xRD7d6ftnxTtPuHclFW9drZPbHs9brC93fabp2wz1NfN9sdsP2j7prbbVtq+wvZPi/9XdKmd9j06oL79le1bi+/bxbaXd6md9j1QK0OYHY2IiyNiTUQsiIjDI+Ilxe2bI+Ks4us7IuIZxeWpEfGXfXh22atrFtc9h4v2yeLe+lPbHJ6mf83KYnK41uqaw0Xbtc5icnhWfaptFs+JHJayz+KBTAzYHpX0QUlnSjpJ0rm2T5qy2ZmS1haX8yV9aBB96WJc0lsi4imSniPpjzr0T5K+FxEnF5d3D7F/Uuu8kyd3OTBFJa9dRNx24PWQ9MuSdkm6uMOmw3zdPiHpjCm3vU3StyNiraRvF9cfp8f36CD6doWkp0XEL0m6XdKfT1M/3XugPmqybApPVPMsziGHJbK4F59QfXO4W/+alcXkcG3VPIelPLKYHO7NJ1TfLO7Ut2blsJR9Fg9qxcCpkjYWsxX7JF0k6ewp25wt6cJo+YGk5baPHFB/Hici7ouI64uvd0jaIGn1MNruk8peuzYvlPSziLhryO0+TrSOrrl1ys1nS/pk8fUnJf16h9Je3qN971tEXB4R48XVH0ha0882hy4kTUZvF1ShtlncgByWyGJJ9c7hbv1rVBaTw3VX2xyWGpHF5HChzlnc+ByWGpHFg5oYWC3pnrbrm/TEkOllm4GzfZykUyRd3eHu59q+0fY3bD91iN0KTX/eyTq8dudI+myX+6p63Q44PCLuk1ofeJIO67BNHV7D35P0jS73zfQeqImQYrK3C6qQRRbXNIclsjhFLjksZZ/F5HDNZZHDUm2zmBxOk0sWZ57DUhOyeFCnK3SH26ZOj/SyzUDZXirpS5LeHBHbp9x9vaRjI2Kn7bMkfUWtZUrDMNN5Jyt97WzPl/QKdV7yU+XrNhtVv4bvUGv53qe7bJLHeaBDyQdRwUDVPotrnMMSWTxodRgH5J/F5HDd1T6HpVpnMTk8eFW/hvnnsNSILB7UioFNko5uu75G0uYS2wyM7TG1AvDTEfHlqfdHxPaI2Fl8famkMdurhtG3aDvvpFr7K506ZZNKXzu19kG6PiIemHpHla9bmwcOLCMr/n+wwzaVvYa2XyfpZZJ+O6LzjkY9vAfqI/P9qRqu1llc5xwu2iSLy6t1DksNy2JyuM5qncNSvbOYHE5W6yxuVA5L2WfxoCYGrpG01vbxxUzaOZIumbLNJZJe65bnSNp2YKnLoNm2pI9K2hAR7+2yzRHFdrJ9qlqv1cND6Fsv552s7LUrnKsuS6aqet2muETS64qvXyfpqx226eU92ne2z5D0Z5JeERG7umyT13mgMw/BhqttFtc5h4v2yOI0tc1hqYFZTA7XWW1zWKp3FpPDfVHbLG5cDkvZZ/FAdiWIiHHbF0i6TNKopI9FxM2231Dc/2FJl0o6S9JGtY7k+fpB9KWL50k6T9JPbN9Q3PZ2Sce09e/Vkv7A9rik3ZLO6TaT1WeHS7q4yJF5kj4TEd+sy2tne7GkF0n6v9pua+/bUF8325+VdJqkVW6d0/Odkt4j6fO2/5OkuyW9ptj2KEkfiYizur1Hh9C3P5e0QK2lUJL0g4h4Q3vf1OU90M++9U+9A26uq3kW1zmHJbJ4Nn2pbQ5P078GZTE5XGc1z2Gp3llMDs+uP7XN4ubnsNSELPbwxlgAmubgscPiP6x6TU/bfvP+v78u6n6aGQDIDDkMANVrQhYP6uCDAOYKJhcBoFrkMABUL/MsZmIAQILI/gisAJA3chgAqpd/FjMxAKC8kKLG52MFgMYjhwGgeg3IYiYGAKSZzHvZFABkjxwGgOplnsVMDABIk/n+VACQPXIYAKqXeRYzMQCgvAhpMu9lUwCQNXIYAKrXgCxmYgBAmsxnRwEge+QwAFQv8yxmYgBAglBMTFTdCQCYw8hhAKhe/lnMxACA8kLZH2gFALJGDgNA9RqQxSNVdwBA5mKyt0sC239l+1bbP7Z9se3lXbY7w/ZttjfafltSowCQC3IYAKqXeRYzMQCgtJAUk9HTJdEVkp4WEb8k6XZJfz51A9ujkj4o6UxJJ0k61/ZJqQ0DQJ2RwwBQvSZkMRMDAMqLGMrsaERcHhHjxdUfSFrTYbNTJW2MiDsiYp+kiySdndQwANQdOQwA1WtAFnOMAQBJKjjQyu9J+lyH21dLuqft+iZJzx5KjwCgQuQwAFQv9yxmYgBAaTv0yGXfii+u6nHzhbavbbu+PiLWH7hi+1uSjuhQ946I+GqxzTskjUv6dIft3OG2vI8CAwAzIIcBoHpNyGImBgCUFhFn9PGxTp/uftuvk/QySS+M6Hii2E2Sjm67vkbS5n71DwDqiBwGgOo1IYs5xgCA2rN9hqQ/k/SKiNjVZbNrJK21fbzt+ZLOkXTJsPoIAE1GDgNA9QaZxUwMAMjBByQtk3SF7Rtsf1iSbB9l+1JJKg7EcoGkyyRtkPT5iLi5qg4DQMOQwwBQvYFlsTuvPgAAAAAAAHMBKwYAAAAAAJjDmBgAAAAAAGAOY2IAAAAAAIA5jIkBAAAAAADmMCYGAAAAAACYw5gYAAAAAABgDmNiAAAAAACAOYyJAQAAAAAA5rD/Hz/Asjzc/+2jAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1296x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_truth_car_vae(y_data, y_truth, mean_post_pred_vae, ttl1=\"data (truth + noise)\", ttl2=\"truth\", ttl3=\"VAE estimate\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "ad4b21fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'VAE post. predictive')"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mx = np.max([y_truth, mean_post_pred_vae])\n",
    "plt.rcParams[\"figure.figsize\"] = (4,4)\n",
    "plt.scatter(y_truth, mean_post_pred_vae)\n",
    "plt.ylim(0, mx+0.1)\n",
    "plt.xlim(0, mx+0.1)\n",
    "plt.axline((1, 1), slope=1, ls=\"--\", c=\".3\")\n",
    "plt.xlabel(\"y-true\")\n",
    "plt.ylabel(\"VAE post. predictive\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "1141d6df",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.13461307\n"
     ]
    }
   ],
   "source": [
    "MSE_vae = np.mean((y_truth -  mean_post_pred_vae)**2)\n",
    "print(MSE_vae)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "853d87b7",
   "metadata": {},
   "source": [
    "## Inference with CAR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "19aef535",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "sample: 100%|███████████████████████████████████████████████| 3000/3000 [00:44<00:00, 67.60it/s, 15 steps of size 2.96e-01. acc. prob=0.89]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                      mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
      "           alpha      0.88      0.07      0.90      0.79      0.99   1884.69      1.00\n",
      "          car[0]     -0.69      0.35     -0.69     -1.27     -0.12   3177.42      1.00\n",
      "          car[1]      0.33      0.35      0.33     -0.24      0.88   3030.66      1.00\n",
      "          car[2]      0.80      0.34      0.81      0.25      1.38   2306.83      1.00\n",
      "          car[3]      0.48      0.34      0.49     -0.09      1.01   3437.17      1.00\n",
      "          car[4]     -0.79      0.35     -0.80     -1.41     -0.28   3175.64      1.00\n",
      "          car[5]     -0.88      0.34     -0.88     -1.41     -0.34   2966.70      1.00\n",
      "          car[6]     -0.89      0.33     -0.90     -1.39     -0.31   3348.38      1.00\n",
      "          car[7]     -0.97      0.35     -0.96     -1.58     -0.44   2404.15      1.00\n",
      "          car[8]     -0.15      0.34     -0.15     -0.72      0.42   4858.64      1.00\n",
      "          car[9]      0.66      0.34      0.67      0.09      1.20   2170.68      1.00\n",
      "         car[10]     -0.18      0.34     -0.18     -0.73      0.38   3411.46      1.00\n",
      "         car[11]     -0.27      0.34     -0.28     -0.82      0.28   3179.68      1.00\n",
      "         car[12]      0.36      0.34      0.36     -0.16      0.96   2227.93      1.00\n",
      "         car[13]     -0.57      0.33     -0.57     -1.13     -0.04   3898.92      1.00\n",
      "         car[14]     -0.47      0.36     -0.46     -1.11      0.07   3137.67      1.00\n",
      "         car[15]     -0.56      0.33     -0.56     -1.08     -0.00   3453.47      1.00\n",
      "         car[16]      0.01      0.32      0.00     -0.51      0.53   3257.57      1.00\n",
      "         car[17]     -0.12      0.33     -0.13     -0.63      0.43   3690.08      1.00\n",
      "         car[18]     -0.26      0.33     -0.26     -0.78      0.29   4098.75      1.00\n",
      "         car[19]     -0.37      0.33     -0.37     -0.92      0.18   2851.97      1.00\n",
      "         car[20]     -0.33      0.32     -0.33     -0.86      0.13   3910.75      1.00\n",
      "         car[21]     -0.37      0.31     -0.38     -0.85      0.16   3913.47      1.00\n",
      "         car[22]     -0.37      0.33     -0.37     -0.90      0.17   3388.64      1.00\n",
      "         car[23]     -0.23      0.33     -0.23     -0.76      0.31   3293.39      1.00\n",
      "         car[24]      0.27      0.33      0.28     -0.29      0.80   2849.87      1.00\n",
      "         car[25]     -0.94      0.31     -0.95     -1.44     -0.41   1624.28      1.00\n",
      "         car[26]     -0.00      0.34     -0.00     -0.56      0.54   2775.86      1.00\n",
      "         car[27]     -0.39      0.32     -0.39     -0.94      0.11   2734.96      1.00\n",
      "         car[28]     -0.83      0.34     -0.84     -1.37     -0.27   2920.17      1.00\n",
      "         car[29]     -0.97      0.34     -0.97     -1.53     -0.42   3104.04      1.00\n",
      "         car[30]     -0.58      0.35     -0.59     -1.11      0.01   4801.64      1.00\n",
      "         car[31]     -0.49      0.32     -0.50     -1.03      0.02   3404.03      1.00\n",
      "         car[32]      0.12      0.32      0.11     -0.40      0.64   3720.81      1.00\n",
      "         car[33]     -0.11      0.33     -0.11     -0.65      0.43   3481.32      1.00\n",
      "         car[34]      0.61      0.32      0.62      0.06      1.13   2783.14      1.00\n",
      "         car[35]      1.00      0.33      1.00      0.52      1.57   1748.78      1.00\n",
      "         car[36]     -0.04      0.31     -0.04     -0.59      0.45   4496.68      1.00\n",
      "         car[37]      0.02      0.33      0.03     -0.54      0.52   3082.02      1.00\n",
      "         car[38]     -0.31      0.34     -0.32     -0.85      0.25   3425.96      1.00\n",
      "         car[39]     -0.52      0.34     -0.52     -1.05      0.02   3767.80      1.00\n",
      "         car[40]     -1.32      0.35     -1.33     -1.92     -0.77   2164.10      1.00\n",
      "         car[41]     -1.19      0.33     -1.19     -1.70     -0.63   3405.66      1.00\n",
      "         car[42]     -1.42      0.35     -1.43     -2.01     -0.87   1859.35      1.00\n",
      "         car[43]     -1.57      0.34     -1.58     -2.14     -1.02   1435.53      1.00\n",
      "         car[44]     -1.15      0.34     -1.15     -1.70     -0.60   2882.50      1.00\n",
      "         car[45]     -0.92      0.35     -0.92     -1.48     -0.36   2120.63      1.00\n",
      "         car[46]     -0.18      0.32     -0.18     -0.70      0.32   3524.29      1.00\n",
      "         car[47]      0.39      0.34      0.39     -0.14      0.94   2255.66      1.00\n",
      "         car[48]     -0.23      0.32     -0.23     -0.77      0.29   3028.49      1.00\n",
      "         car[49]      0.14      0.33      0.13     -0.35      0.73   4244.02      1.00\n",
      "         car[50]      0.79      0.33      0.80      0.25      1.33   1944.25      1.00\n",
      "         car[51]     -0.69      0.35     -0.70     -1.20     -0.09   2071.75      1.00\n",
      "         car[52]     -0.76      0.34     -0.76     -1.31     -0.24   2948.41      1.00\n",
      "         car[53]     -1.12      0.36     -1.14     -1.72     -0.55   1231.85      1.00\n",
      "         car[54]      0.09      0.34      0.10     -0.48      0.65   2951.79      1.00\n",
      "         car[55]     -0.67      0.32     -0.67     -1.18     -0.14   3397.28      1.00\n",
      "         car[56]     -1.21      0.33     -1.22     -1.72     -0.66   3166.74      1.00\n",
      "         car[57]     -1.09      0.33     -1.09     -1.61     -0.53   2832.49      1.00\n",
      "         car[58]     -0.97      0.32     -0.98     -1.46     -0.41   2901.86      1.00\n",
      "         car[59]     -0.79      0.34     -0.79     -1.35     -0.23   2615.37      1.00\n",
      "         car[60]     -0.62      0.35     -0.63     -1.17     -0.03   3749.65      1.00\n",
      "         car[61]     -0.31      0.32     -0.30     -0.81      0.23   3617.50      1.00\n",
      "         car[62]      0.32      0.33      0.32     -0.25      0.86   3626.41      1.00\n",
      "         car[63]      0.44      0.33      0.46     -0.06      1.03   3187.05      1.00\n",
      "         car[64]      1.06      0.32      1.06      0.57      1.58   1568.51      1.00\n",
      "         car[65]      0.41      0.32      0.40     -0.16      0.90   3304.67      1.00\n",
      "         car[66]      0.34      0.32      0.35     -0.18      0.85   3480.46      1.00\n",
      "         car[67]     -0.43      0.33     -0.43     -0.98      0.10   3070.29      1.00\n",
      "         car[68]      0.33      0.31      0.34     -0.22      0.81   2153.65      1.00\n",
      "         car[69]      0.48      0.33      0.49     -0.08      1.01   2132.05      1.00\n",
      "         car[70]     -0.54      0.33     -0.53     -1.08      0.00   2962.57      1.00\n",
      "         car[71]     -0.79      0.33     -0.79     -1.25     -0.19   2798.46      1.00\n",
      "         car[72]     -0.61      0.32     -0.61     -1.14     -0.09   3438.09      1.00\n",
      "         car[73]     -0.82      0.34     -0.82     -1.42     -0.32   3157.99      1.00\n",
      "         car[74]     -0.37      0.34     -0.37     -0.91      0.21   2681.35      1.00\n",
      "         car[75]      0.41      0.35      0.42     -0.14      0.96   3058.23      1.00\n",
      "         car[76]      0.30      0.31      0.30     -0.21      0.80   3512.50      1.00\n",
      "         car[77]      1.38      0.34      1.39      0.83      1.93   1099.30      1.00\n",
      "         car[78]     -0.10      0.33     -0.11     -0.63      0.46   2698.47      1.00\n",
      "         car[79]     -0.21      0.33     -0.22     -0.76      0.32   2614.82      1.00\n",
      "         car[80]      0.72      0.34      0.74      0.18      1.29   3746.56      1.00\n",
      "         car[81]      0.79      0.34      0.80      0.23      1.34   2654.71      1.00\n",
      "         car[82]      0.59      0.34      0.59      0.05      1.19   2770.98      1.00\n",
      "         car[83]     -0.28      0.31     -0.29     -0.73      0.29   2398.55      1.00\n",
      "         car[84]     -0.18      0.32     -0.19     -0.73      0.34   3631.31      1.00\n",
      "         car[85]     -0.09      0.35     -0.10     -0.70      0.43   3855.13      1.00\n",
      "         car[86]     -0.67      0.32     -0.67     -1.17     -0.10   2825.84      1.00\n",
      "         car[87]      0.14      0.34      0.15     -0.41      0.69   3625.02      1.00\n",
      "         car[88]      0.01      0.32      0.01     -0.49      0.55   4049.15      1.00\n",
      "         car[89]     -0.27      0.34     -0.27     -0.84      0.28   3147.74      1.00\n",
      "         car[90]     -0.28      0.35     -0.28     -0.83      0.28   2788.16      1.00\n",
      "         car[91]      0.55      0.33      0.56      0.05      1.12   2818.48      1.00\n",
      "         car[92]      0.82      0.33      0.82      0.26      1.34   2976.02      1.00\n",
      "         car[93]      0.11      0.31      0.11     -0.40      0.62   3839.49      1.00\n",
      "         car[94]     -0.36      0.33     -0.37     -0.85      0.21   2773.32      1.00\n",
      "         car[95]      0.58      0.31      0.57      0.10      1.10   3956.25      1.00\n",
      "         car[96]      0.25      0.32      0.26     -0.30      0.75   3213.06      1.00\n",
      "         car[97]      0.30      0.31      0.30     -0.18      0.81   3852.37      1.00\n",
      "         car[98]      0.45      0.32      0.45     -0.07      1.00   2451.52      1.00\n",
      "         car[99]     -0.16      0.32     -0.17     -0.66      0.41   3963.20      1.00\n",
      "        car[100]     -0.51      0.33     -0.52     -1.04      0.03   3020.82      1.00\n",
      "        car[101]     -0.32      0.33     -0.32     -0.85      0.22   3508.27      1.00\n",
      "        car[102]      0.22      0.33      0.23     -0.35      0.73   2845.53      1.00\n",
      "        car[103]      0.30      0.33      0.31     -0.29      0.80   2971.07      1.00\n",
      "        car[104]      0.58      0.33      0.58      0.08      1.17   3372.52      1.00\n",
      "        car[105]      1.08      0.36      1.10      0.47      1.64   1538.31      1.00\n",
      "        car[106]     -0.17      0.32     -0.17     -0.69      0.32   3361.67      1.00\n",
      "        car[107]      0.03      0.31      0.02     -0.51      0.52   3850.31      1.00\n",
      "        car[108]     -0.44      0.33     -0.46     -0.94      0.13   1783.88      1.00\n",
      "        car[109]      0.35      0.31      0.35     -0.17      0.87   3133.95      1.00\n",
      "        car[110]      0.43      0.31      0.43     -0.08      0.92   3562.20      1.00\n",
      "        car[111]      0.15      0.32      0.15     -0.35      0.70   3536.40      1.00\n",
      "        car[112]     -0.07      0.34     -0.08     -0.55      0.53   3616.70      1.00\n",
      "        car[113]      0.17      0.31      0.16     -0.30      0.70   3134.87      1.00\n",
      "        car[114]      0.43      0.33      0.43     -0.13      0.98   3543.03      1.00\n",
      "        car[115]     -0.11      0.32     -0.12     -0.61      0.44   3722.68      1.00\n",
      "        car[116]     -0.40      0.32     -0.39     -0.91      0.14   2546.22      1.00\n",
      "        car[117]     -0.09      0.31     -0.09     -0.60      0.42   2931.45      1.00\n",
      "        car[118]      0.03      0.33      0.03     -0.47      0.60   3406.26      1.00\n",
      "        car[119]      0.56      0.33      0.57      0.05      1.13   2308.97      1.00\n",
      "        car[120]      0.24      0.37      0.25     -0.30      0.89   3274.23      1.00\n",
      "        car[121]     -0.57      0.33     -0.56     -1.06      0.02   2424.22      1.00\n",
      "        car[122]     -0.58      0.32     -0.58     -1.12     -0.08   3068.28      1.00\n",
      "        car[123]      0.10      0.34      0.11     -0.44      0.65   3452.04      1.00\n",
      "        car[124]      0.18      0.33      0.18     -0.37      0.69   4017.61      1.00\n",
      "        car[125]      0.38      0.33      0.38     -0.18      0.89   3734.98      1.00\n",
      "        car[126]      0.27      0.32      0.27     -0.26      0.75   3509.53      1.00\n",
      "        car[127]      0.18      0.33      0.17     -0.36      0.67   3272.26      1.00\n",
      "        car[128]      0.41      0.33      0.42     -0.16      0.93   3531.19      1.00\n",
      "        car[129]     -0.26      0.34     -0.26     -0.81      0.30   3701.05      1.00\n",
      "        car[130]     -0.02      0.34     -0.01     -0.58      0.52   3558.13      1.00\n",
      "        car[131]     -0.45      0.31     -0.44     -0.97      0.07   3362.50      1.00\n",
      "        car[132]      0.54      0.32      0.55      0.06      1.10   2122.20      1.00\n",
      "        car[133]      0.10      0.33      0.10     -0.46      0.59   3659.76      1.00\n",
      "        car[134]     -0.30      0.34     -0.30     -0.88      0.24   3474.09      1.00\n",
      "        car[135]     -0.05      0.38     -0.06     -0.62      0.62   4025.82      1.00\n",
      "        car[136]     -0.23      0.35     -0.23     -0.84      0.34   3604.92      1.00\n",
      "        car[137]     -0.61      0.34     -0.61     -1.17     -0.10   2813.97      1.00\n",
      "        car[138]     -0.71      0.35     -0.73     -1.31     -0.16   3058.85      1.00\n",
      "        car[139]      0.04      0.34      0.04     -0.48      0.61   3050.15      1.00\n",
      "        car[140]      0.61      0.35      0.62      0.02      1.16   4182.00      1.00\n",
      "        car[141]      0.81      0.36      0.82      0.28      1.44   3384.08      1.00\n",
      "        car[142]     -0.00      0.34     -0.00     -0.53      0.57   3205.20      1.00\n",
      "        car[143]      0.01      0.34      0.01     -0.56      0.58   3683.88      1.00\n",
      "        car[144]     -0.71      0.34     -0.72     -1.29     -0.18   3455.23      1.00\n",
      "        car[145]     -0.61      0.34     -0.62     -1.19     -0.07   2876.44      1.00\n",
      "        car[146]     -0.26      0.34     -0.25     -0.88      0.26   3479.34      1.00\n",
      "        car[147]      0.32      0.33      0.32     -0.23      0.87   3238.98      1.00\n",
      "        car[148]      0.49      0.34      0.50     -0.07      1.08   3481.65      1.00\n",
      "        car[149]     -0.56      0.37     -0.56     -1.20      0.01   4261.81      1.00\n",
      "  car_samples[0]     -0.69      0.35     -0.69     -1.27     -0.12   3177.42      1.00\n",
      "  car_samples[1]      0.33      0.35      0.33     -0.24      0.88   3030.66      1.00\n",
      "  car_samples[2]      0.80      0.34      0.81      0.25      1.38   2306.83      1.00\n",
      "  car_samples[3]      0.48      0.34      0.49     -0.09      1.01   3437.17      1.00\n",
      "  car_samples[4]     -0.79      0.35     -0.80     -1.41     -0.28   3175.64      1.00\n",
      "  car_samples[5]     -0.88      0.34     -0.88     -1.41     -0.34   2966.70      1.00\n",
      "  car_samples[6]     -0.89      0.33     -0.90     -1.39     -0.31   3348.38      1.00\n",
      "  car_samples[7]     -0.97      0.35     -0.96     -1.58     -0.44   2404.15      1.00\n",
      "  car_samples[8]     -0.15      0.34     -0.15     -0.72      0.42   4858.64      1.00\n",
      "  car_samples[9]      0.66      0.34      0.67      0.09      1.20   2170.68      1.00\n",
      " car_samples[10]     -0.18      0.34     -0.18     -0.73      0.38   3411.46      1.00\n",
      " car_samples[11]     -0.27      0.34     -0.28     -0.82      0.28   3179.68      1.00\n",
      " car_samples[12]      0.36      0.34      0.36     -0.16      0.96   2227.93      1.00\n",
      " car_samples[13]     -0.57      0.33     -0.57     -1.13     -0.04   3898.92      1.00\n",
      " car_samples[14]     -0.47      0.36     -0.46     -1.11      0.07   3137.67      1.00\n",
      " car_samples[15]     -0.56      0.33     -0.56     -1.08     -0.00   3453.47      1.00\n",
      " car_samples[16]      0.01      0.32      0.00     -0.51      0.53   3257.57      1.00\n",
      " car_samples[17]     -0.12      0.33     -0.13     -0.63      0.43   3690.08      1.00\n",
      " car_samples[18]     -0.26      0.33     -0.26     -0.78      0.29   4098.75      1.00\n",
      " car_samples[19]     -0.37      0.33     -0.37     -0.92      0.18   2851.97      1.00\n",
      " car_samples[20]     -0.33      0.32     -0.33     -0.86      0.13   3910.75      1.00\n",
      " car_samples[21]     -0.37      0.31     -0.38     -0.85      0.16   3913.47      1.00\n",
      " car_samples[22]     -0.37      0.33     -0.37     -0.90      0.17   3388.64      1.00\n",
      " car_samples[23]     -0.23      0.33     -0.23     -0.76      0.31   3293.39      1.00\n",
      " car_samples[24]      0.27      0.33      0.28     -0.29      0.80   2849.87      1.00\n",
      " car_samples[25]     -0.94      0.31     -0.95     -1.44     -0.41   1624.28      1.00\n",
      " car_samples[26]     -0.00      0.34     -0.00     -0.56      0.54   2775.86      1.00\n",
      " car_samples[27]     -0.39      0.32     -0.39     -0.94      0.11   2734.96      1.00\n",
      " car_samples[28]     -0.83      0.34     -0.84     -1.37     -0.27   2920.17      1.00\n",
      " car_samples[29]     -0.97      0.34     -0.97     -1.53     -0.42   3104.04      1.00\n",
      " car_samples[30]     -0.58      0.35     -0.59     -1.11      0.01   4801.64      1.00\n",
      " car_samples[31]     -0.49      0.32     -0.50     -1.03      0.02   3404.03      1.00\n",
      " car_samples[32]      0.12      0.32      0.11     -0.40      0.64   3720.81      1.00\n",
      " car_samples[33]     -0.11      0.33     -0.11     -0.65      0.43   3481.32      1.00\n",
      " car_samples[34]      0.61      0.32      0.62      0.06      1.13   2783.14      1.00\n",
      " car_samples[35]      1.00      0.33      1.00      0.52      1.57   1748.78      1.00\n",
      " car_samples[36]     -0.04      0.31     -0.04     -0.59      0.45   4496.68      1.00\n",
      " car_samples[37]      0.02      0.33      0.03     -0.54      0.52   3082.02      1.00\n",
      " car_samples[38]     -0.31      0.34     -0.32     -0.85      0.25   3425.96      1.00\n",
      " car_samples[39]     -0.52      0.34     -0.52     -1.05      0.02   3767.80      1.00\n",
      " car_samples[40]     -1.32      0.35     -1.33     -1.92     -0.77   2164.10      1.00\n",
      " car_samples[41]     -1.19      0.33     -1.19     -1.70     -0.63   3405.66      1.00\n",
      " car_samples[42]     -1.42      0.35     -1.43     -2.01     -0.87   1859.35      1.00\n",
      " car_samples[43]     -1.57      0.34     -1.58     -2.14     -1.02   1435.53      1.00\n",
      " car_samples[44]     -1.15      0.34     -1.15     -1.70     -0.60   2882.50      1.00\n",
      " car_samples[45]     -0.92      0.35     -0.92     -1.48     -0.36   2120.63      1.00\n",
      " car_samples[46]     -0.18      0.32     -0.18     -0.70      0.32   3524.29      1.00\n",
      " car_samples[47]      0.39      0.34      0.39     -0.14      0.94   2255.66      1.00\n",
      " car_samples[48]     -0.23      0.32     -0.23     -0.77      0.29   3028.49      1.00\n",
      " car_samples[49]      0.14      0.33      0.13     -0.35      0.73   4244.02      1.00\n",
      " car_samples[50]      0.79      0.33      0.80      0.25      1.33   1944.25      1.00\n",
      " car_samples[51]     -0.69      0.35     -0.70     -1.20     -0.09   2071.75      1.00\n",
      " car_samples[52]     -0.76      0.34     -0.76     -1.31     -0.24   2948.41      1.00\n",
      " car_samples[53]     -1.12      0.36     -1.14     -1.72     -0.55   1231.85      1.00\n",
      " car_samples[54]      0.09      0.34      0.10     -0.48      0.65   2951.79      1.00\n",
      " car_samples[55]     -0.67      0.32     -0.67     -1.18     -0.14   3397.28      1.00\n",
      " car_samples[56]     -1.21      0.33     -1.22     -1.72     -0.66   3166.74      1.00\n",
      " car_samples[57]     -1.09      0.33     -1.09     -1.61     -0.53   2832.49      1.00\n",
      " car_samples[58]     -0.97      0.32     -0.98     -1.46     -0.41   2901.86      1.00\n",
      " car_samples[59]     -0.79      0.34     -0.79     -1.35     -0.23   2615.37      1.00\n",
      " car_samples[60]     -0.62      0.35     -0.63     -1.17     -0.03   3749.65      1.00\n",
      " car_samples[61]     -0.31      0.32     -0.30     -0.81      0.23   3617.50      1.00\n",
      " car_samples[62]      0.32      0.33      0.32     -0.25      0.86   3626.41      1.00\n",
      " car_samples[63]      0.44      0.33      0.46     -0.06      1.03   3187.05      1.00\n",
      " car_samples[64]      1.06      0.32      1.06      0.57      1.58   1568.51      1.00\n",
      " car_samples[65]      0.41      0.32      0.40     -0.16      0.90   3304.67      1.00\n",
      " car_samples[66]      0.34      0.32      0.35     -0.18      0.85   3480.46      1.00\n",
      " car_samples[67]     -0.43      0.33     -0.43     -0.98      0.10   3070.29      1.00\n",
      " car_samples[68]      0.33      0.31      0.34     -0.22      0.81   2153.65      1.00\n",
      " car_samples[69]      0.48      0.33      0.49     -0.08      1.01   2132.05      1.00\n",
      " car_samples[70]     -0.54      0.33     -0.53     -1.08      0.00   2962.57      1.00\n",
      " car_samples[71]     -0.79      0.33     -0.79     -1.25     -0.19   2798.46      1.00\n",
      " car_samples[72]     -0.61      0.32     -0.61     -1.14     -0.09   3438.09      1.00\n",
      " car_samples[73]     -0.82      0.34     -0.82     -1.42     -0.32   3157.99      1.00\n",
      " car_samples[74]     -0.37      0.34     -0.37     -0.91      0.21   2681.35      1.00\n",
      " car_samples[75]      0.41      0.35      0.42     -0.14      0.96   3058.23      1.00\n",
      " car_samples[76]      0.30      0.31      0.30     -0.21      0.80   3512.50      1.00\n",
      " car_samples[77]      1.38      0.34      1.39      0.83      1.93   1099.30      1.00\n",
      " car_samples[78]     -0.10      0.33     -0.11     -0.63      0.46   2698.47      1.00\n",
      " car_samples[79]     -0.21      0.33     -0.22     -0.76      0.32   2614.82      1.00\n",
      " car_samples[80]      0.72      0.34      0.74      0.18      1.29   3746.56      1.00\n",
      " car_samples[81]      0.79      0.34      0.80      0.23      1.34   2654.71      1.00\n",
      " car_samples[82]      0.59      0.34      0.59      0.05      1.19   2770.98      1.00\n",
      " car_samples[83]     -0.28      0.31     -0.29     -0.73      0.29   2398.55      1.00\n",
      " car_samples[84]     -0.18      0.32     -0.19     -0.73      0.34   3631.31      1.00\n",
      " car_samples[85]     -0.09      0.35     -0.10     -0.70      0.43   3855.13      1.00\n",
      " car_samples[86]     -0.67      0.32     -0.67     -1.17     -0.10   2825.84      1.00\n",
      " car_samples[87]      0.14      0.34      0.15     -0.41      0.69   3625.02      1.00\n",
      " car_samples[88]      0.01      0.32      0.01     -0.49      0.55   4049.15      1.00\n",
      " car_samples[89]     -0.27      0.34     -0.27     -0.84      0.28   3147.74      1.00\n",
      " car_samples[90]     -0.28      0.35     -0.28     -0.83      0.28   2788.16      1.00\n",
      " car_samples[91]      0.55      0.33      0.56      0.05      1.12   2818.48      1.00\n",
      " car_samples[92]      0.82      0.33      0.82      0.26      1.34   2976.02      1.00\n",
      " car_samples[93]      0.11      0.31      0.11     -0.40      0.62   3839.49      1.00\n",
      " car_samples[94]     -0.36      0.33     -0.37     -0.85      0.21   2773.32      1.00\n",
      " car_samples[95]      0.58      0.31      0.57      0.10      1.10   3956.25      1.00\n",
      " car_samples[96]      0.25      0.32      0.26     -0.30      0.75   3213.06      1.00\n",
      " car_samples[97]      0.30      0.31      0.30     -0.18      0.81   3852.37      1.00\n",
      " car_samples[98]      0.45      0.32      0.45     -0.07      1.00   2451.52      1.00\n",
      " car_samples[99]     -0.16      0.32     -0.17     -0.66      0.41   3963.20      1.00\n",
      "car_samples[100]     -0.51      0.33     -0.52     -1.04      0.03   3020.82      1.00\n",
      "car_samples[101]     -0.32      0.33     -0.32     -0.85      0.22   3508.27      1.00\n",
      "car_samples[102]      0.22      0.33      0.23     -0.35      0.73   2845.53      1.00\n",
      "car_samples[103]      0.30      0.33      0.31     -0.29      0.80   2971.07      1.00\n",
      "car_samples[104]      0.58      0.33      0.58      0.08      1.17   3372.52      1.00\n",
      "car_samples[105]      1.08      0.36      1.10      0.47      1.64   1538.31      1.00\n",
      "car_samples[106]     -0.17      0.32     -0.17     -0.69      0.32   3361.67      1.00\n",
      "car_samples[107]      0.03      0.31      0.02     -0.51      0.52   3850.31      1.00\n",
      "car_samples[108]     -0.44      0.33     -0.46     -0.94      0.13   1783.88      1.00\n",
      "car_samples[109]      0.35      0.31      0.35     -0.17      0.87   3133.95      1.00\n",
      "car_samples[110]      0.43      0.31      0.43     -0.08      0.92   3562.20      1.00\n",
      "car_samples[111]      0.15      0.32      0.15     -0.35      0.70   3536.40      1.00\n",
      "car_samples[112]     -0.07      0.34     -0.08     -0.55      0.53   3616.70      1.00\n",
      "car_samples[113]      0.17      0.31      0.16     -0.30      0.70   3134.87      1.00\n",
      "car_samples[114]      0.43      0.33      0.43     -0.13      0.98   3543.03      1.00\n",
      "car_samples[115]     -0.11      0.32     -0.12     -0.61      0.44   3722.68      1.00\n",
      "car_samples[116]     -0.40      0.32     -0.39     -0.91      0.14   2546.22      1.00\n",
      "car_samples[117]     -0.09      0.31     -0.09     -0.60      0.42   2931.45      1.00\n",
      "car_samples[118]      0.03      0.33      0.03     -0.47      0.60   3406.26      1.00\n",
      "car_samples[119]      0.56      0.33      0.57      0.05      1.13   2308.97      1.00\n",
      "car_samples[120]      0.24      0.37      0.25     -0.30      0.89   3274.23      1.00\n",
      "car_samples[121]     -0.57      0.33     -0.56     -1.06      0.02   2424.22      1.00\n",
      "car_samples[122]     -0.58      0.32     -0.58     -1.12     -0.08   3068.28      1.00\n",
      "car_samples[123]      0.10      0.34      0.11     -0.44      0.65   3452.04      1.00\n",
      "car_samples[124]      0.18      0.33      0.18     -0.37      0.69   4017.61      1.00\n",
      "car_samples[125]      0.38      0.33      0.38     -0.18      0.89   3734.98      1.00\n",
      "car_samples[126]      0.27      0.32      0.27     -0.26      0.75   3509.53      1.00\n",
      "car_samples[127]      0.18      0.33      0.17     -0.36      0.67   3272.26      1.00\n",
      "car_samples[128]      0.41      0.33      0.42     -0.16      0.93   3531.19      1.00\n",
      "car_samples[129]     -0.26      0.34     -0.26     -0.81      0.30   3701.05      1.00\n",
      "car_samples[130]     -0.02      0.34     -0.01     -0.58      0.52   3558.13      1.00\n",
      "car_samples[131]     -0.45      0.31     -0.44     -0.97      0.07   3362.50      1.00\n",
      "car_samples[132]      0.54      0.32      0.55      0.06      1.10   2122.20      1.00\n",
      "car_samples[133]      0.10      0.33      0.10     -0.46      0.59   3659.76      1.00\n",
      "car_samples[134]     -0.30      0.34     -0.30     -0.88      0.24   3474.09      1.00\n",
      "car_samples[135]     -0.05      0.38     -0.06     -0.62      0.62   4025.82      1.00\n",
      "car_samples[136]     -0.23      0.35     -0.23     -0.84      0.34   3604.92      1.00\n",
      "car_samples[137]     -0.61      0.34     -0.61     -1.17     -0.10   2813.97      1.00\n",
      "car_samples[138]     -0.71      0.35     -0.73     -1.31     -0.16   3058.85      1.00\n",
      "car_samples[139]      0.04      0.34      0.04     -0.48      0.61   3050.15      1.00\n",
      "car_samples[140]      0.61      0.35      0.62      0.02      1.16   4182.00      1.00\n",
      "car_samples[141]      0.81      0.36      0.82      0.28      1.44   3384.08      1.00\n",
      "car_samples[142]     -0.00      0.34     -0.00     -0.53      0.57   3205.20      1.00\n",
      "car_samples[143]      0.01      0.34      0.01     -0.56      0.58   3683.88      1.00\n",
      "car_samples[144]     -0.71      0.34     -0.72     -1.29     -0.18   3455.23      1.00\n",
      "car_samples[145]     -0.61      0.34     -0.62     -1.19     -0.07   2876.44      1.00\n",
      "car_samples[146]     -0.26      0.34     -0.25     -0.88      0.26   3479.34      1.00\n",
      "car_samples[147]      0.32      0.33      0.32     -0.23      0.87   3238.98      1.00\n",
      "car_samples[148]      0.49      0.34      0.50     -0.07      1.08   3481.65      1.00\n",
      "car_samples[149]     -0.56      0.37     -0.56     -1.20      0.01   4261.81      1.00\n",
      "           noise      0.41      0.06      0.41      0.31      0.51    181.18      1.01\n",
      "\n",
      "Number of divergences: 0\n"
     ]
    }
   ],
   "source": [
    "#args[\"y\"] = y_true\n",
    "\n",
    "# inference - smooth data and infer alpha\n",
    "start = time.time()\n",
    "init_strategy = init_to_median(num_samples=10)\n",
    "kernel = NUTS(CAR_model, init_strategy=init_strategy)\n",
    "mcmc = MCMC(kernel, num_warmup=1000, num_samples=2000)\n",
    "rng_key, rng_key_infer = random.split(rng_key)\n",
    "mcmc.run(rng_key_infer, args, y=y_data)\n",
    "mcmc_samples = mcmc.get_samples()\n",
    "mcmc.print_summary(exclude_deterministic=False)\n",
    "t_elapsed = time.time() - start"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "2aedcab0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MCMC elapsed time: 47 s\n",
      "Average ESS for all CAR effects : 3128\n"
     ]
    }
   ],
   "source": [
    "print(\"\\nMCMC elapsed time:\", round(t_elapsed), \"s\")\n",
    "\n",
    "ss = numpyro.diagnostics.summary(mcmc.get_samples(group_by_chain=True))\n",
    "r = np.mean(ss['car']['n_eff'])\n",
    "print(\"Average ESS for all CAR effects : \" + str(round(r)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "a8c0b0ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['alpha', 'car', 'car_samples', 'noise'])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mcmc_samples.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "2b469fab",
   "metadata": {},
   "outputs": [],
   "source": [
    "# posterior predictive\n",
    "rng_key, rng_key_predict = random.split(rng_key)\n",
    "posterior_predictive = Predictive(CAR_model, mcmc_samples)\n",
    "posterior_predictions = posterior_predictive(rng_key_predict, args, y=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "1235a20f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1296x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "post_obs = posterior_predictions['car_samples']\n",
    "mean_post_pred_car = np.mean(post_obs, axis=0)\n",
    "hpdi_post_pred_car = hpdi(post_obs, 0.9)\n",
    "\n",
    "plot_truth_car_vae(y_data, \n",
    "                   y_truth, \n",
    "                   mean_post_pred_car, \n",
    "                   ttl1=\"data (truth + noise)\", \n",
    "                   ttl2=\"truth\", \n",
    "                   ttl3=\"CAR estimate\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "b66e3366",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.118769534\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mx = np.max([y_truth, mean_post_pred_car])\n",
    "plt.rcParams[\"figure.figsize\"] = (4,4)\n",
    "plt.scatter(y_truth, mean_post_pred_car)\n",
    "plt.ylim(0, mx+0.1)\n",
    "plt.xlim(0, mx+0.1)\n",
    "plt.axline((1, 1), slope=1, ls=\"--\", c=\".3\")\n",
    "plt.xlabel(\"y-true\")\n",
    "plt.ylabel(\"CAR post. predictive\")\n",
    "\n",
    "MSE_car = np.mean((y_truth -  mean_post_pred_car)**2)\n",
    "print(MSE_car)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "0dd656f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'CAR post. predictive')"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mx = np.max([ mean_post_pred_vae, mean_post_pred_car])\n",
    "plt.rcParams[\"figure.figsize\"] = (4,4)\n",
    "plt.scatter(mean_post_pred_vae, mean_post_pred_car)\n",
    "plt.ylim(0, mx+0.1)\n",
    "plt.xlim(0, mx+0.1)\n",
    "plt.axline((1, 1), slope=1, ls=\"--\", c=\".3\")\n",
    "plt.xlabel(\"VAE post. predictive\")\n",
    "plt.ylabel(\"CAR post. predictive\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "8b19ce00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1296x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1296x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_truth_car_vae(y_data, \n",
    "                   y_truth, \n",
    "                   mean_post_pred_vae, \n",
    "                   ttl1=\"data (truth + noise)\", \n",
    "                   ttl2=\"truth\", \n",
    "                   ttl3=\"VAE estimate\")\n",
    "\n",
    "plot_truth_car_vae(y_data, \n",
    "                   y_truth, \n",
    "                   mean_post_pred_car, \n",
    "                   ttl1=\"data (truth + noise)\", \n",
    "                   ttl2=\"truth\", \n",
    "                   ttl3=\"CAR estimate\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "be87ee26",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_data_truth_car_vae(y_data, y_true, mean_post_pred_car, mean_post_pred_vae, \n",
    "                       ttl1=\"Data\", ttl2=\"Ground truth\", ttl3=\"CAR estimate\", ttl4=\"VAE-CAR estimate\"):\n",
    "    fig, axs = plt.subplots(2, 2, figsize=(12, 8))\n",
    "    _min = np.amin([y_data, y_true, mean_post_pred_car, mean_post_pred_vae])\n",
    "    _max = np.amax([y_data, y_true, mean_post_pred_car, mean_post_pred_vae])\n",
    "\n",
    "    im = axs[0,0].imshow(y_data.reshape(ny, nx), \n",
    "                       cmap='inferno', \n",
    "                       interpolation='none', \n",
    "                       origin='lower',\n",
    "                       vmin=_min, vmax=_max)\n",
    "    fig.colorbar(im, ax=axs[0,0])\n",
    "    axs[0,0].set_title(ttl1)  \n",
    "\n",
    "    im = axs[0,1].imshow(y_true.reshape(ny, nx), \n",
    "                       cmap='inferno', \n",
    "                       interpolation='none', \n",
    "                       origin='lower',\n",
    "                       vmin=_min, vmax=_max)\n",
    "\n",
    "    fig.colorbar(im, ax=axs[0,1])\n",
    "    axs[0,1].set_title(ttl2)\n",
    "    \n",
    "    im = axs[1,0].imshow(mean_post_pred_car.reshape(ny, nx), \n",
    "                       cmap='inferno', \n",
    "                       interpolation='none', \n",
    "                       origin='lower',\n",
    "                       vmin=_min, vmax=_max)\n",
    "\n",
    "    fig.colorbar(im, ax=axs[1,0])\n",
    "    axs[1,0].set_title(ttl3)\n",
    "    \n",
    "    im = axs[1,1].imshow(mean_post_pred_vae.reshape(ny, nx), \n",
    "                       cmap='inferno', \n",
    "                       interpolation='none', \n",
    "                       origin='lower',\n",
    "                       vmin=_min, vmax=_max)\n",
    "\n",
    "    fig.colorbar(im, ax=axs[1,1])\n",
    "    axs[1,1].set_title(ttl4)\n",
    "    \n",
    "    return fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "3b304b8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 8 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plot_data_truth_car_vae(y_data, \n",
    "                        y_truth, \n",
    "                        mean_post_pred_car,\n",
    "                        mean_post_pred_vae)\n",
    "\n",
    "#plt.rcParams['figure.dpi'] = 300\n",
    "#plt.rcParams['savefig.dpi'] = 300\n",
    "#fig.savefig(\"../res/synth_CAR.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "353400b9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}