From c9e834db69683b2f8c1656af2ac0c390ee8777f4 Mon Sep 17 00:00:00 2001 From: mitch-at-orika Date: Sat, 9 Dec 2023 09:22:57 +1000 Subject: [PATCH 1/2] one constant as zero --- .../GLM-discrete-choice_models.ipynb | 1781 +++++++---------- 1 file changed, 746 insertions(+), 1035 deletions(-) diff --git a/examples/generalized_linear_models/GLM-discrete-choice_models.ipynb b/examples/generalized_linear_models/GLM-discrete-choice_models.ipynb index 41931e47e..f94ea942d 100644 --- a/examples/generalized_linear_models/GLM-discrete-choice_models.ipynb +++ b/examples/generalized_linear_models/GLM-discrete-choice_models.ipynb @@ -196,14 +196,14 @@ "\n", "$$ \\text{softmax}(u)_{j} = \\frac{\\exp(u_{j})}{\\sum_{q=1}^{J}\\exp(u_{q})} $$\n", "\n", - "The model then assumes that decision maker chooses the option that maximises their subjective utility. The individual utility functions can be richly parameterised. The model is identified just when the utility measures of the alternatives are benchmarked against the fixed utility of the \"outside good.\" The last quantity is fixed at 0. \n", + "The model then assumes that decision maker chooses the option that maximises their subjective utility. The individual utility functions can be richly parameterised. When contants are included, one alternative's constant must be fixed at 0 in order to normalise the overall level of the constants. \n", "\n", "$$\\begin{pmatrix}\n", "u_{gc} \\\\\n", "u_{gr} \\\\\n", "u_{ec} \\\\\n", "u_{er} \\\\\n", - "0 \\\\\n", + "u_{hp} \\\\\n", "\\end{pmatrix}\n", "$$\n", "\n", @@ -379,23 +379,16 @@ "output_type": "stream", "text": [ "Sampling: [beta_ic, beta_oc, y_cat]\n", - "/Users/nathanielforde/mambaforge/envs/pymc_examples_new/lib/python3.9/site-packages/pymc/sampling/mcmc.py:243: UserWarning: Use of external NUTS sampler is still experimental\n", - " warnings.warn(\"Use of external NUTS sampler is still experimental\", UserWarning)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ "Compiling...\n", - "Compilation time = 0:00:01.199248\n", + "An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.\n", + "Compilation time = 0:00:01.806791\n", "Sampling...\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "258e7c249c4d4353a285ee1640c3a58b", + "model_id": "a93fafe587e84dc0beb31d9222eca911", "version_major": 2, "version_minor": 0 }, @@ -409,7 +402,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "9755fcd74e784c93a56d1563a6fd714c", + "model_id": "bddaf80409b24c6ca3ea21e8a0fa350e", "version_major": 2, "version_minor": 0 }, @@ -423,7 +416,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "40d5abd188bd4f69af0e1b3602b3514b", + "model_id": "0c9e8311ef3145c4b5af75e49b96b924", "version_major": 2, "version_minor": 0 }, @@ -437,7 +430,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "9aa8dd4eff7345449b2afb4924577136", + "model_id": "5fec714b5e8e47e4a9268f369fe90b33", "version_major": 2, "version_minor": 0 }, @@ -449,93 +442,139 @@ "output_type": "display_data" }, { - "name": "stdout", + "name": "stderr", "output_type": "stream", "text": [ - "Sampling time = 0:00:02.165671\n", + "Sampling time = 0:00:03.589848\n", "Transforming variables...\n", - "Transformation time = 0:00:00.404064\n", - "Computing Log Likelihood...\n" + "Transformation time = 0:00:00.487455\n", + "Computing Log Likelihood...\n", + "Log Likelihood time = 0:00:00.660260\n", + "Sampling: [y_cat]\n" ] }, + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + "
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\n", + " " + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, { "data": { "image/svg+xml": [ "\n", "\n", - "\n", "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", "\n", "clusterobs (900) x alts_probs (5)\n", - "\n", - "obs (900) x alts_probs (5)\n", + "\n", + "obs (900) x alts_probs (5)\n", "\n", "\n", "clusterobs (900)\n", - "\n", - "obs (900)\n", + "\n", + "obs (900)\n", "\n", - "\n", + "\n", "\n", - "beta_oc\n", - "\n", - "beta_oc\n", - "~\n", - "Normal\n", + "beta_ic\n", + "\n", + "beta_ic\n", + "~\n", + "Normal\n", "\n", "\n", "\n", "p\n", - "\n", - "p\n", - "~\n", - "Deterministic\n", + "\n", + "p\n", + "~\n", + "Deterministic\n", "\n", - "\n", + "\n", "\n", - "beta_oc->p\n", - "\n", - "\n", + "beta_ic->p\n", + "\n", + "\n", "\n", - "\n", + "\n", "\n", - "beta_ic\n", - "\n", - "beta_ic\n", - "~\n", - "Normal\n", + "beta_oc\n", + "\n", + "beta_oc\n", + "~\n", + "Normal\n", "\n", - "\n", + "\n", "\n", - "beta_ic->p\n", - "\n", - "\n", + "beta_oc->p\n", + "\n", + "\n", "\n", "\n", "\n", "y_cat\n", - "\n", - "y_cat\n", - "~\n", - "Categorical\n", + "\n", + "y_cat\n", + "~\n", + "Categorical\n", "\n", "\n", "\n", "p->y_cat\n", - "\n", - "\n", + "\n", + "\n", "\n", "\n", "\n" ], "text/plain": [ - "" + "" ] }, "execution_count": 5, @@ -560,7 +599,7 @@ " u1 = beta_ic * wide_heating_df[\"ic.er\"] + beta_oc * wide_heating_df[\"oc.er\"]\n", " u2 = beta_ic * wide_heating_df[\"ic.gc\"] + beta_oc * wide_heating_df[\"oc.gc\"]\n", " u3 = beta_ic * wide_heating_df[\"ic.gr\"] + beta_oc * wide_heating_df[\"oc.gr\"]\n", - " u4 = np.zeros(N) # Outside Good\n", + " u4 = beta_ic * wide_heating_df[\"ic.hp\"] + beta_oc * wide_heating_df[\"oc.hp\"]#np.zeros(N) # Outside Good\n", " s = pm.math.stack([u0, u1, u2, u3, u4]).T\n", "\n", " ## Apply Softmax Transform\n", @@ -594,8 +633,8 @@ "
    \n", " \n", "
  • \n", - " \n", - " \n", + " \n", + " \n", "
    \n", "
    \n", "
      \n", @@ -970,79 +1009,79 @@ " * obs (obs) int64 0 1 2 3 4 5 6 7 ... 892 893 894 895 896 897 898 899\n", " * alts_probs (alts_probs) <U2 'ec' 'er' 'gc' 'gr' 'hp'\n", "Data variables:\n", - " beta_ic (chain, draw) float64 0.001854 0.001794 ... 0.002087 0.001928\n", - " beta_oc (chain, draw) float64 -0.003802 -0.003846 ... -0.00447 -0.004533\n", - " p (chain, draw, obs, alts_probs) float64 0.07322 0.1129 ... 0.1111\n", + " beta_ic (chain, draw) float64 -0.006063 -0.006218 ... -0.005608\n", + " beta_oc (chain, draw) float64 -0.004401 -0.00453 ... -0.004273 -0.004928\n", + " p (chain, draw, obs, alts_probs) float64 0.09993 ... 0.02927\n", "Attributes:\n", - " created_at: 2023-07-13T17:29:12.988497\n", - " arviz_version: 0.15.1
    • chain
      PandasIndex
      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='chain'))
    • draw
      PandasIndex
      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
      +       "       ...\n",
      +       "       990, 991, 992, 993, 994, 995, 996, 997, 998, 999],\n",
      +       "      dtype='int64', name='draw', length=1000))
    • obs
      PandasIndex
      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
      +       "       ...\n",
      +       "       890, 891, 892, 893, 894, 895, 896, 897, 898, 899],\n",
      +       "      dtype='int64', name='obs', length=900))
    • alts_probs
      PandasIndex
      PandasIndex(Index(['ec', 'er', 'gc', 'gr', 'hp'], dtype='object', name='alts_probs'))
  • created_at :
    2023-12-08T23:15:51.335704
    arviz_version :
    0.16.1

\n", " \n", " \n", " \n", " \n", "
  • \n", - " \n", - " \n", + " \n", + " \n", "
    \n", "
    \n", "
      \n", @@ -1416,55 +1455,55 @@ " * draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 992 993 994 995 996 997 998 999\n", " * obs (obs) int64 0 1 2 3 4 5 6 7 8 ... 892 893 894 895 896 897 898 899\n", "Data variables:\n", - " y_cat (chain, draw, obs) int64 4 3 4 2 2 1 1 2 4 1 ... 4 3 2 1 4 2 1 1 0\n", + " y_cat (chain, draw, obs) int64 4 2 2 3 3 3 3 3 4 2 ... 2 0 3 0 2 2 2 2 2\n", "Attributes:\n", - " created_at: 2023-07-13T17:29:19.656809\n", - " arviz_version: 0.15.1\n", + " created_at: 2023-12-08T23:16:02.315123\n", + " arviz_version: 0.16.1\n", " inference_library: pymc\n", - " inference_library_version: 5.3.0
    • chain
      PandasIndex
      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='chain'))
    • draw
      PandasIndex
      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
      +       "       ...\n",
      +       "       990, 991, 992, 993, 994, 995, 996, 997, 998, 999],\n",
      +       "      dtype='int64', name='draw', length=1000))
    • obs
      PandasIndex
      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
      +       "       ...\n",
      +       "       890, 891, 892, 893, 894, 895, 896, 897, 898, 899],\n",
      +       "      dtype='int64', name='obs', length=900))
  • created_at :
    2023-12-08T23:16:02.315123
    arviz_version :
    0.16.1
    inference_library :
    pymc
    inference_library_version :
    5.9.2

  • \n", " \n", " \n", " \n", " \n", "
  • \n", - " \n", - " \n", + " \n", + " \n", "
    \n", "
    \n", "
      \n", @@ -1839,63 +1878,63 @@ " * y_cat_dim_0 (y_cat_dim_0) int64 0\n", " * y_cat_dim_1 (y_cat_dim_1) int64 0 1 2 3 4 5 6 ... 894 895 896 897 898 899\n", "Data variables:\n", - " y_cat (chain, draw, y_cat_dim_0, y_cat_dim_1) float64 -1.258 ... -...\n", + " y_cat (chain, draw, y_cat_dim_0, y_cat_dim_1) float64 -0.7837 ... ...\n", "Attributes:\n", - " created_at: 2023-07-13T17:29:12.992158\n", - " arviz_version: 0.15.1
    • chain
      PandasIndex
      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='chain'))
    • draw
      PandasIndex
      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
      +       "       ...\n",
      +       "       990, 991, 992, 993, 994, 995, 996, 997, 998, 999],\n",
      +       "      dtype='int64', name='draw', length=1000))
    • y_cat_dim_0
      PandasIndex
      PandasIndex(Index([0], dtype='int64', name='y_cat_dim_0'))
    • y_cat_dim_1
      PandasIndex
      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
      +       "       ...\n",
      +       "       890, 891, 892, 893, 894, 895, 896, 897, 898, 899],\n",
      +       "      dtype='int64', name='y_cat_dim_1', length=900))
  • created_at :
    2023-12-08T23:15:51.341719
    arviz_version :
    0.16.1

  • \n", " \n", " \n", " \n", " \n", "
  • \n", - " \n", - " \n", + " \n", + " \n", "
    \n", "
    \n", "
      \n", @@ -2268,63 +2307,63 @@ " * chain (chain) int64 0 1 2 3\n", " * draw (draw) int64 0 1 2 3 4 5 6 ... 993 994 995 996 997 998 999\n", "Data variables:\n", - " acceptance_rate (chain, draw) float64 0.9667 1.0 0.8868 ... 0.8931 0.9283\n", - " step_size (chain, draw) float64 0.02965 0.02965 ... 0.03209 0.03209\n", + " acceptance_rate (chain, draw) float64 0.9776 1.0 0.9124 ... 0.7537 0.9359\n", + " step_size (chain, draw) float64 0.08947 0.08947 ... 0.09163 0.09163\n", " diverging (chain, draw) bool False False False ... False False False\n", - " energy (chain, draw) float64 1.311e+03 1.311e+03 ... 1.312e+03\n", - " n_steps (chain, draw) int64 3 3 3 3 1 11 3 7 3 ... 7 7 7 11 7 3 7 3\n", - " tree_depth (chain, draw) int64 2 2 2 2 1 4 2 3 2 ... 2 3 3 3 4 3 2 3 2\n", - " lp (chain, draw) float64 1.311e+03 1.311e+03 ... 1.311e+03\n", + " energy (chain, draw) float64 1.098e+03 1.097e+03 ... 1.099e+03\n", + " n_steps (chain, draw) int64 3 3 3 3 3 3 3 3 3 ... 3 3 3 3 3 3 3 3 3\n", + " tree_depth (chain, draw) int64 2 2 2 2 2 2 2 2 2 ... 2 2 2 2 2 2 2 2 2\n", + " lp (chain, draw) float64 1.097e+03 1.097e+03 ... 1.099e+03\n", "Attributes:\n", - " created_at: 2023-07-13T17:29:12.990891\n", - " arviz_version: 0.15.1
    • energy
      (chain, draw)
      float64
      1.098e+03 1.097e+03 ... 1.099e+03
      array([[1097.90950349, 1097.36422046, 1097.76408102, ..., 1100.39503349,\n",
      +       "        1098.66672608, 1098.67424013],\n",
      +       "       [1098.15388719, 1099.27908376, 1101.08526536, ..., 1097.31659306,\n",
      +       "        1097.91532156, 1097.65291876],\n",
      +       "       [1098.06289565, 1103.8600668 , 1099.18136448, ..., 1097.52624159,\n",
      +       "        1097.43840975, 1097.17355288],\n",
      +       "       [1097.82568096, 1097.8691726 , 1098.61066406, ..., 1100.02872094,\n",
      +       "        1099.40014771, 1099.31391116]])
    • n_steps
      (chain, draw)
      int64
      3 3 3 3 3 3 3 3 ... 3 3 3 3 3 3 3 3
      array([[3, 3, 3, ..., 3, 7, 7],\n",
      +       "       [3, 3, 3, ..., 3, 3, 3],\n",
      +       "       [7, 3, 3, ..., 3, 3, 1],\n",
      +       "       [3, 7, 1, ..., 3, 3, 3]])
    • tree_depth
      (chain, draw)
      int64
      2 2 2 2 2 2 2 2 ... 2 2 2 2 2 2 2 2
      array([[2, 2, 2, ..., 2, 3, 3],\n",
      +       "       [2, 2, 2, ..., 2, 2, 2],\n",
      +       "       [3, 2, 2, ..., 2, 2, 1],\n",
      +       "       [2, 3, 1, ..., 2, 2, 2]])
    • lp
      (chain, draw)
      float64
      1.097e+03 1.097e+03 ... 1.099e+03
      array([[1097.36089423, 1097.08832319, 1097.08832319, ..., 1097.64865711,\n",
      +       "        1097.51831863, 1097.38555111],\n",
      +       "       [1097.13634355, 1098.64597557, 1097.73482937, ..., 1097.26878686,\n",
      +       "        1097.39788158, 1097.37262558],\n",
      +       "       [1098.04342905, 1099.26550485, 1097.25738844, ..., 1097.52383524,\n",
      +       "        1097.16505449, 1097.14329955],\n",
      +       "       [1097.7304434 , 1097.86798173, 1098.53144277, ..., 1097.15469481,\n",
      +       "        1098.15374095, 1099.14610513]])
    • chain
      PandasIndex
      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='chain'))
    • draw
      PandasIndex
      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
      +       "       ...\n",
      +       "       990, 991, 992, 993, 994, 995, 996, 997, 998, 999],\n",
      +       "      dtype='int64', name='draw', length=1000))
  • created_at :
    2023-12-08T23:15:51.339556
    arviz_version :
    0.16.1

  • \n", " \n", " \n", " \n", " \n", "
  • \n", - " \n", - " \n", + " \n", + " \n", "
    \n", "
    \n", "
      \n", @@ -2699,147 +2738,147 @@ " * obs (obs) int64 0 1 2 3 4 5 6 7 ... 892 893 894 895 896 897 898 899\n", " * alts_probs (alts_probs) <U2 'ec' 'er' 'gc' 'gr' 'hp'\n", "Data variables:\n", - " beta_oc (chain, draw) float64 0.05221 0.1678 0.7865 ... 0.5232 -0.09242\n", - " p (chain, draw, obs, alts_probs) float64 4.778e-201 ... 4.831e-91\n", - " beta_ic (chain, draw) float64 -0.57 -0.8283 0.2129 ... 1.097 0.2006\n", + " beta_ic (chain, draw) float64 -1.975 -1.131 1.304 ... 1.736 -1.448\n", + " p (chain, draw, obs, alts_probs) float64 1.526e-134 ... 0.0\n", + " beta_oc (chain, draw) float64 -0.9053 0.7179 -0.3289 ... 0.2239 -2.288\n", "Attributes:\n", - " created_at: 2023-07-13T17:29:07.842667\n", - " arviz_version: 0.15.1\n", + " created_at: 2023-12-08T23:15:43.538814\n", + " arviz_version: 0.16.1\n", " inference_library: pymc\n", - " inference_library_version: 5.3.0
    • chain
      PandasIndex
      PandasIndex(Index([0], dtype='int64', name='chain'))
    • draw
      PandasIndex
      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
      +       "       ...\n",
      +       "       490, 491, 492, 493, 494, 495, 496, 497, 498, 499],\n",
      +       "      dtype='int64', name='draw', length=500))
    • obs
      PandasIndex
      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
      +       "       ...\n",
      +       "       890, 891, 892, 893, 894, 895, 896, 897, 898, 899],\n",
      +       "      dtype='int64', name='obs', length=900))
    • alts_probs
      PandasIndex
      PandasIndex(Index(['ec', 'er', 'gc', 'gr', 'hp'], dtype='object', name='alts_probs'))
  • created_at :
    2023-12-08T23:15:43.538814
    arviz_version :
    0.16.1
    inference_library :
    pymc
    inference_library_version :
    5.9.2

  • \n", " \n", " \n", " \n", " \n", "
  • \n", - " \n", - " \n", + " \n", + " \n", "
    \n", "
    \n", "
      \n", @@ -3213,31 +3252,31 @@ " * draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499\n", " * obs (obs) int64 0 1 2 3 4 5 6 7 8 ... 892 893 894 895 896 897 898 899\n", "Data variables:\n", - " y_cat (chain, draw, obs) int64 4 4 4 4 4 4 4 4 4 4 ... 3 1 1 3 3 3 3 3 3\n", + " y_cat (chain, draw, obs) int64 2 2 2 3 2 2 2 2 2 2 ... 2 3 2 2 2 2 2 2 2\n", "Attributes:\n", - " created_at: 2023-07-13T17:29:07.844409\n", - " arviz_version: 0.15.1\n", + " created_at: 2023-12-08T23:15:43.547264\n", + " arviz_version: 0.16.1\n", " inference_library: pymc\n", - " inference_library_version: 5.3.0
    • chain
      PandasIndex
      PandasIndex(Index([0], dtype='int64', name='chain'))
    • draw
      PandasIndex
      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
      +       "       ...\n",
      +       "       490, 491, 492, 493, 494, 495, 496, 497, 498, 499],\n",
      +       "      dtype='int64', name='draw', length=500))
    • obs
      PandasIndex
      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
      +       "       ...\n",
      +       "       890, 891, 892, 893, 894, 895, 896, 897, 898, 899],\n",
      +       "      dtype='int64', name='obs', length=900))
  • created_at :
    2023-12-08T23:15:43.547264
    arviz_version :
    0.16.1
    inference_library :
    pymc
    inference_library_version :
    5.9.2

  • \n", " \n", " \n", " \n", " \n", "
  • \n", - " \n", - " \n", + " \n", + " \n", "
    \n", "
    \n", "
      \n", @@ -3611,10 +3650,10 @@ "Data variables:\n", " y_cat (obs) int64 2 2 2 1 1 2 2 2 2 2 2 2 2 ... 2 2 2 2 2 2 2 1 2 2 2 2 2\n", "Attributes:\n", - " created_at: 2023-07-13T17:29:07.844758\n", - " arviz_version: 0.15.1\n", + " created_at: 2023-12-08T23:15:43.551429\n", + " arviz_version: 0.16.1\n", " inference_library: pymc\n", - " inference_library_version: 5.3.0
    • obs
      PandasIndex
      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
      +       "       ...\n",
      +       "       890, 891, 892, 893, 894, 895, 896, 897, 898, 899],\n",
      +       "      dtype='int64', name='obs', length=900))
  • created_at :
    2023-12-08T23:15:43.551429
    arviz_version :
    0.16.1
    inference_library :
    pymc
    inference_library_version :
    5.9.2

  • \n", " \n", " \n", " \n", @@ -4065,26 +4104,26 @@ " \n", " \n", " beta_ic\n", - " 0.002\n", + " -0.006\n", " 0.0\n", - " 0.002\n", - " 0.002\n", + " -0.007\n", + " -0.006\n", " 0.0\n", " 0.0\n", - " 1870.0\n", - " 1999.0\n", + " 3471.0\n", + " 2790.0\n", " 1.0\n", " \n", " \n", " beta_oc\n", - " -0.004\n", + " -0.005\n", " 0.0\n", " -0.005\n", " -0.004\n", " 0.0\n", " 0.0\n", - " 881.0\n", - " 1105.0\n", + " 3971.0\n", + " 2946.0\n", " 1.0\n", " \n", " \n", @@ -4093,8 +4132,8 @@ ], "text/plain": [ " mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail \\\n", - "beta_ic 0.002 0.0 0.002 0.002 0.0 0.0 1870.0 1999.0 \n", - "beta_oc -0.004 0.0 -0.005 -0.004 0.0 0.0 881.0 1105.0 \n", + "beta_ic -0.006 0.0 -0.007 -0.006 0.0 0.0 3471.0 2790.0 \n", + "beta_oc -0.005 0.0 -0.005 -0.004 0.0 0.0 3971.0 2946.0 \n", "\n", " r_hat \n", "beta_ic 1.0 \n", @@ -4137,7 +4176,7 @@ { "data": { "text/plain": [ - "-2.215565260325244" + "0.7380233924649465" ] }, "execution_count": 8, @@ -4166,7 +4205,7 @@ "outputs": [ { "data": { - "image/png": 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t2rQin3mFfa8AMHfuXMF1ma/gc6MkpINpY2JiSjxmUUaPHo3AwEBJec+ePXB1dVW6f2H3KlUFBwdj7dq1gvUUZGFhgX79+uG7775T+Z0hOjoaW7ZswZkzZ/Dhw4dC2+rq6qJevXro3LkzBg4cKPNO37lzZ0RHR8vtW/B9Qh55368yzwfpd5WCoqOjizy3Hz9+XOh4xTmHlTl31H2vKum6c3JycOTIERw4cACPHj1S2M7a2ho9e/bEN998AysrK6XHL+w7OXPmDDZu3CjzW+SzsLDA2LFj4e7uDgMDA6XnJCIiIiIiIiIiIiKiPNplvQAiIiIiIiIiIiIiIiJN2LFjBwYPHgx/f3+5ge1AXnZTLy8v9OvXDw8ePFB5jqioKAwbNgzjx4/HpUuXCg1sB/ICb318fDBt2jQcP35cqTm2b9+Orl27YteuXYUGtgPAkydPsGDBAvTr1w9RUVFKfw5pWVlZ+OWXXzBp0iS5ge2adPHiRbRv3x6//vor/P39Cw1sB/ICfu/fv4/Zs2dj+PDhpRJYJu3EiRPo06cPTp48qTBYLycnBz4+Phg4cCAuX76s8TU1a9YM9erVk5RTUlKUPuekHTx4UFDu3bu32gLb1Sk0NBR9+/bF1q1bFQa2A3mbXowbNw5///13Ka5OyMXFRZBB/tixY0VmHA4ICBAE5/Xt27fYWUrj4+PRqlUrfP/99zh+/HiRge1AXjDeqlWr0KNHD9y8ebNY8xa0du1aDB8+HFeuXFF4j5bn4sWL6NmzJzw9PeUGtgN594UbN25g5MiRZfo7A5q9PwwbNgxff/019u3bV2RgO5CXOd7DwwM9e/bEgQMHlJ7nYyIvkF2ZTOUHDhxAly5dsGrVKty4caPQwHYAyM7ORmBgICZPnozJkycrHUCvCXFxcZg8eTJGjRoFPz+/Qt9FMjMz4efnh0GDBmHJkiXIyckplTUmJSVhypQpcHd3x7Vr1xReCwCQmpqKs2fPon///liyZAmys7NLZY3FUaFCBUFZmXfBT8WGDRswatQohYHtAJCQkIDdu3ejV69eKr1Penp6olevXvj333+LDGwH8t5b7969izVr1uD06dNKz0PlW3h4OHr37o358+cXGtgO5G2MtWfPHnTp0gWenp4lmjc9PR2zZs3CjBkzFAa2A3nn9+rVqzFq1KhibzRERERERERERERERPQ5Y3A7ERERERERERERERF9cjZu3IiVK1cKgrZ0dHRgYWEhN7N3fHw8xo8fj7i4OKXnuHHjBgYNGqQwWEckEsHCwgJ6enpyjxcVyJqVlYW5c+fijz/+QGpqqsxxXV1dWFhYQFdXV+ZYeHg4hg4ditDQUCU+iaz58+fj8OHDgjqRSARzc/NiB9MqKyUlRWGgq76+PiwsLKCvry/3+J07dzBkyBDExsZqcokCR48exezZswWBkNra2jA3N5f726SlpWHq1Kl4+vSpxtc2cuRIQVk6SF0ZCQkJMoFiBbO4lxdhYWEYM2aMTGZWU1NThdk0161bhyNHjpTG8mRoaWmhX79+knJ0dDSCgoIK7XP06FFBuX///sWePzs7W2EAZv69xcjISO7x9+/f4+uvv0ZAQECx51+3bh02btwouA/mXzfy7tH5/Pz8MH36dLnBjvL6i8VirFu3Djt27Cj2WktC0/cHRZs4aGtrw9TUFGZmZtDWlv0nAVlZWVi8eDE2b96s5Cf5eISFhcnU2dnZFdmvsI1UDA0NFT5vgbwNF0aNGlVkQLwmREREYMiQIbh48aLc44aGhjAzM5N5dovFYuzfvx/Tpk3TePD427dvMWLECPj5+ck9bmRkJPc+nZubi/3792Pq1Kll8t0qw9nZWVCOjY3Fzz//jIyMjDJaUenYsWMH1q9fL7iHi0QiuecakJfRfsKECbhz506RYx8/fhzz5s2T+5vnz1HY9UifhuDgYIwYMQIRERFyj5uZmUFHR0emPiUlBfPmzcP69euLNW9OTg6mT5+OkydPCur19PRgZmYmt8+9e/fw3XffFfnfdkREREREREREREREJCT7//QTERERERERERERERF9xK5evYrbt28DACwsLDB27Fh07doVNWvWhJaWFnJychASEoJNmzbhypUrkn7x8fH4/fff8fvvvxc5R3h4OL755huZoHMnJyeMGDECrVu3RpUqVSQBPgkJCXj48CGuXr2KM2fO4OXLl0XO8dtvv8HLy0tQV7duXYwaNQqtWrWCvb29pP7p06c4ffo0du3aJckeGxsbi++++w5eXl4qZdk+c+aMJAOwqakpxo4dix49eki+v6ysLDx69AjPnj0DACxatEjSt+Cf5ZWlWVhYKDxmZmaGdu3aoW3btqhXrx5q1qwpCGqPi4tDSEgIjhw5ggsXLkjq37x5g//973+lEswaFhaGkydPQiwWw9DQEKNGjUKvXr3g6OgIbW1tiMViPHjwAP/88w9OnDgh6ZeZmYmFCxdi3759csdV13fap08f/PHHH5JA4NDQUISEhKBJkyZKf0Zvb29BkJ6zszPq16+vdP/SkJ6eLgl41tLSQq9evTB48GA0bdpUcs5ERUXB29sb27dvF3yeFStWoEuXLjA3Ny/1dffv3x8bN26UlL29veHi4iK3bX4m43xNmjRBjRo1SrwGXV1duLi4oH379mjQoAHq1KkjCN5KTU3Fw4cPcfr0aXh6ekq+u6ysLPzwww84fvw4LC0tVZrz7t27kkB9fX19jBw5Er1790a9evWgra2NnJwcREREIDg4WNDv1atX+OGHHwQZn7W0tDBgwAAMGTIEDRs2hI6ODnJychAWFgZvb2/s378f2dnZ+Ouvv1C3bt1ifkvFo6n7gzz169dHx44d0aRJE9SpUwdffPGF5PmTnZ2NJ0+ewM/PD/v378e7d+8k/datW4fmzZujefPm6vvgZezMmTOCsra2Nho3bqx0/4oVK6J9+/Zo06YN6tati+rVqwuCaN+8eYObN2/i4MGDgozVoaGhWLZsGX799Ve543bs2BEVK1YEkBcMXzAYvWPHjujYsaPCNSm61hMSEjB+/Hi8evVKUicSidCjRw/0798fTZs2lTz/MzIycOvWLezbtw/nz5+XtPfz88OaNWswe/ZsxV9KCeTk5GDmzJkymw44ODhg8uTJ6Nixo+T+GxMTAx8fH2zatAnv37+XtPX391f43Rb8XoG8DSXy3wGBvPusvN/f2Ni4hJ8sT7du3bBt2zZB3alTp3D//n2MGTMGPXr0gLW1tVrmKi/CwsJw/PhxAHnX19ChQzF48GA4OjpCJBIhMzMTQUFB2L17N/z9/SX9kpOTMW3aNJw6dUphkHBKSgqWLl0qqLO2toa7uzs6duyIatWqCa7HuLg4hIeHIygoCBcvXsS9e/fkjjtz5kykpKQAANasWYOEhATBscLeR6tXr17Y16GQhYWF5J0tISEBa9asERybOXNmscbVNE3cq1QVExODadOmyWzg0qFDB4waNQotW7aEnp4ecnNz8fTpUxw9ehS7d+8WvB9s2LABNWrUQO/evVWae926dZKNy2rWrIkJEyagXbt2+OKLLwDknaOXLl3CmjVrEBkZKekXGBgILy8vfPXVV8X81EREREREREREREREnx8GtxMRERERERERERER0SclPyChcePG2LRpE6ysrATHRSIRmjdvju3bt+Pnn38WBJCfPHkSP/74o0yfgtLS0jB9+nRBYLtIJMIvv/yCESNGyM1YaWFhgdatW6N169aYPXs2Lly4UGggzZkzZ3DgwAFJWUtLCzNmzMDkyZPlZuF1cHDA9OnT0a9fP0yaNEmS5fD58+f466+/sGDBAoVzScsPbK9Tpw527NghCebIp6urC2dnZ0m20uHDh0uOSQdeFzymrEqVKmHZsmXo06ePwgztAGBlZQU3Nze4ubnh4sWLmDlzpiQT9ZUrVxAYGKgwUFhdHjx4ACAv8Gnbtm2oWrWq4LiWlhYaNGiAVatWoXr16tiwYYPkWFBQEEJDQ+Ho6Cgzrrq+UwMDAwwcOBD//POPpO7gwYMqBbf/+++/xZ6/tMTGxiI2NhZGRkZYs2YNOnToINPG3t4e3333HZo3b44JEyYgJycHQF7m62PHjmHMmDGlvWxUq1YNTZs2xa1btwAAZ8+exYIFC2BoaCjT9uzZs4J7TkmytgN5GUi//fZbDB8+HBUqVFDYzsjISBL8PHr0aEycOBEvXrwAALx79w779+/H9OnTVZo7Pyt5pUqVsHPnTjg4OAiOi0Qi1K5dG7Vr1xbUL1y4UBKcmP8ZNmzYIPN7i0Qi1KtXD/Xq1UPv3r0xbtw4JCUlSa7X0qKp+0NB/fv3h5ubm8x3VZCOjg4cHR3h6OiI0aNHY/bs2ZIM2jk5OVi7di327t1b3I9Zrvj5+QmCaQGgXbt2guBnRWrVqoW1a9eia9euEIlECttVqlQJX375Jb788kt4enpi4cKFkvvJ4cOHMWnSJMHmM/kaNmyIhg0bAgDev38vCBht0KBBse6tP/30kyCwvVKlSli7dq3cYG59fX20atUKrVq1wrFjx/Dzzz9LMrZv374d3bp1k8lCrg47duzAzZs3BXX9+vXD0qVLoaenJ6i3sbHBqFGj0KdPH0yePFnyPgcAhw4dQqdOndC5c2dBn4LfKwDcuXNHENzu6uqKgQMHqvETCTk7O6NTp04yWelfvHiBpUuXYtmyZahduzacnZ3RqFEjODs7o3bt2oWeY+Vd/r3N0NAQmzdvRsuWLQXH9fT00KZNG7Rp0wa7du3C8uXLJcfevXuH33//HcuWLZM7tr+/vyDw3N7eHocOHVL4Xm5lZQVXV1e4urpi+vTpCA0NRWZmpky7vn37Sv68bds2wRx9+vSBnZ1dkZ9bVSYmJpLr+uXLl4LgdmNj43L5PgVo5l6lqp9//lnwG2lpaWH+/PkYOXKkoJ22tjZq166NOXPmoE+fPhg3bhxiY2MlxxcuXIgWLVrAxsZG6bnz7ztDhw7FggULZLLDGxsbo2fPnmjTpg1Gjx6N0NBQybF9+/YxuJ2IiIiIiIiIiIiISAWy//qJiIiIiIiIiIiIiIjoI2dra4utW7cWGqSupaWFefPmCYLesrKyBFnA5fn3338FmfqAvOzPI0eOlBvYLm/eLl26KMyUm5OTg5UrVwrqZs2ahW+++UZuYHtB9vb22Lp1K0xNTSV1hw8fRlxcXJHrKsjc3FxuYHtpaNasGQYNGlRoYLu0jh07ygTw79+/X91Lk8vU1BTbt2+XCVyVNm3aNJnM0dIZhjVBesOF06dPCwKGCnP9+nU8e/ZMUjY3N0evXr3UvUS1+f333+UGthfUunVrDBs2TFBXGr+DIgMGDJD8OSUlBT4+PnLbeXt7S/6sp6dX4t/B3Nwc06dPLzSwXVr16tWxZcsWQUCqh4cHcnNzVZ5fV1cXW7ZskQlsV+Tx48e4dOmSoG7x4sVF/t7Ozs5Yu3atyutTF03fH6ZMmVJoYLs0ExMTrFu3TpBdNzAwULKpyccqJycHhw4dwvfffy+o19XVxaxZs5Qao3PnzujRo4dKQceDBw/GN998Iynn5ubCw8ND6f4lcf36dUFAtampKf755x+lstT369dPkKldLBZj+/btal9jeno6duzYIahr2bIlli9fLhPYXpC5uTm2bdsGW1tbQf3GjRvVvkZ1WL58ucJrXCwWIywsDIcPH8b8+fPRr18/NG/eHOPHj8fWrVvx8uXLUl6t+vz2228yge3S3N3d4e7uLqjz9vbGmzdv5LaX3oRkwoQJhb7LS3N0dNTIJg1Ueu7evYsrV64I6qZNmyYT2C7N0dERW7duFQSjJycnY9euXSqvoXPnzliyZIlMYHtBZmZmWLp0qaDu4cOHkg2AiIiIiIiIiIiIiIioaAxuJyIiIiIiIiIiIiKiT87s2bNhbm5eZDtjY2P06dNHUHf//n2F7bOysrBz505BXe/evQUZIUvq9OnTiI6OlpTr16+PCRMmKN3f3t4eX3/9taSckZGBY8eOqbSGqVOnlklge0n0798f1tbWknJAQECpzDt58mS5WXqlaWtrY/DgwYK6ws41dalatSratWsnKWdkZAgCpQsjHaQ5YMAAGBgYqHV96tK+fXt069ZNqbZDhw4VlB89elSsAG116Nmzp2AjB3nX6qtXrxAYGCgpu7m5wczMrFTWJ61mzZpwc3OTlN+/f1+swOhhw4YVmZW8oH///VdQbtSokdLZmNu0aYPu3burtD51KY/3Bz09PYwZM0ZQd+PGDY3MpS4eHh4y/9u/fz+2bt2KuXPnonPnzpg/fz7S0tIkfUQiEX799VeVzrPicHd3h66urqRcWt+ldDD69OnTUbNmTaX7jx49WhCQ7ePjo/JGOEU5fvy4YDMVHR0dLF68WKkNBExNTfHzzz8L6u7duyfI5l5eWFpa4t9//xU8awuTmpqKK1euYNWqVejSpQvGjh2LO3fuaHiV6tWyZUulN1n57rvvBBtJ5W9GIU9iYqKgrImM6lS+7d27V1CuXr06Jk+erFTfBg0ayATBHz58WPBsKIquri4WLlyoVNuGDRuifv36grrSeLcnIiIiIiIiIiIiIvpUMLidiIiIiIiIiIiIiIg+KRYWFioFMjZt2lRQjoiIUNj2zp07iImJEdQVzNqqDidOnBCUR4wYUWTGdmnSAUcFA2OLoquri/79+6s0X3mgra2Nhg0bSsrx8fEaz54oLyC1MKqca+okHehz8OBBiMXiQvu8e/cOvr6+gjrpoPDyRJW11alTByYmJpJyamoqXr9+rYllFcnU1FQQLH7t2jWZe4y3t7fg9yrr61M6M3RxgjKHDBmiUnvpLK6qXHdA2Zy75fn+oI7fsDQtWrRI5n9LlizBqlWr4OXlJZMFumrVqti+fTsGDBig8bWZmpoKgsofP36MjIwMjc4ZFxeHq1evSsoGBgYqXxM6OjqCd6Xc3FzcvHlTbWsEgEuXLgnK7dq1Q/Xq1ZXu7+bmJhPc7O/vr46lqZ2VlRW2b9+OrVu3okWLFtDS0lKqn1gsxrVr1zB06FAsWrQIWVlZGl6pegwfPlzptsbGxujXr5+g7uLFi3LbmpqaCsoMFP78SN83hg4dCj09PaX7jx49WnD9JSYm4vbt20r379ChAypVqqR0+7J6tyciIiIiIiIiIiIi+hTolPUCiIiIiIiIiIiIiIiI1KlZs2ZKZQXNJ51VNykpSWFb6Wzg9evXR61atVRbYCHkBZcpmwm0IAcHBxgYGCA9PR0AVArqqFu3LiwsLFSeU5Nyc3MRFRWF58+fIzk5GSkpKcjOzpZpJ5119tWrV4LMtOpWp04dlb4rVc41dWrfvj3s7e0RFRUFAIiMjMSNGzfQqlUrhX08PT0FQXYtW7ZUKStwadLS0kKLFi1Uam9nZ4fQ0FBJXWn9FvL0798fp06dApB3rh87dgyTJk2SHC+Yzb1ixYpo27atxtby9u1bPH36FImJiUhJSUFmZqbMRgiPHj0SlFXdGMDS0hJ16tRRun18fDyeP38uqGvfvr1Kc7q6ukJfX1/jQccFldX9ISkpCeHh4YiLi0NycjLS09NlfsOC2bQB1X/D8mzixImYMWOGIJt6cWVnZyMyMhLR0dGSZ09OTo5Mu4LnVXZ2Nt6+fSvze6pTcHCw4Ddt2rQpjI2NVR7HyclJUA4JCUHXrl1LvL6C4xWk6thaWlro1q0bdu7cqXDM8qZDhw7o0KEDoqKicOHCBdy4cQO3bt3Chw8fCu0nFovh4eGBqKgobNmyBTo65fef8ujo6KBjx44q9XFzc8OOHTsk5cePHyM9PR0GBgaCds7OzoLyli1bUL16dfTo0aPY66WPR0REhMzzSdX7hr29PZycnPDgwQNJ3a1btwp95y1IlfdJADIbcCQmJqrUn4iIiIiIiIiIiIjoc1Z+/0aMiIiIiIiIiIiIiIioGGxtbVVqLx0QlpycrLDtw4cPBeUmTZqoNFdRnj17JgiK0NHRkcmerSxdXV1JcHtcXByys7OVCpZSJehUk7Kzs3H69GmcPHkSN27cQFpamspjaDpgWZPnmjppa2tj+PDhWLlypaTOw8NDYaBPbm4uPD09BXWqZGktbSYmJjA3N1epT1n9FvK0bdsW1tbWePfuHQAIgttv3rwpCOzu06eP2oMeAwMDcfToUfj6+iI+Pl7l/qoGcql6j5HOgmplZQUbGxuVxtDR0UHt2rVLNQtwad4fnj17Bi8vL5w9e1ZmIwBlfErBeNu2bUNGRgbmzp0LbW1tlfunpaXh+PHjOHHiBG7dulWsTNqafvbcuXNHUM7MzISHh4fK4zx9+lRQzr8HqUNcXJzMeA0aNFB5HOk+jx8/LtG6Sou9vT3c3d3h7u4OAHjx4gXu37+PO3fuICAgQGaTkHxXrlzB6tWrMWfOnFJcrWpq1qwpE5RelHr16kFbWxu5ubkA8t7xnjx5IvP7durUCTY2NoiJiQEApKamYsaMGahVqxZ69uyJ9u3bw8nJqVwH/1PxSV/fFhYWxdoopEGDBoLgdlXuG9LB6kUpT++TREREREREREREREQfG/6NDxERERERERERERERfVJMTU1Vai8d/JYfeCOPdGZwdWdmlQ4Ey87OxqJFi9QydmJiIqysrIpsVx6ytt+6dQvz58/HkydPSjROSkqKmlYkn6rnmkgkEpQLO9fUbdCgQVi3bp1kwwNfX1+8e/cO1tbWMm39/f3x6tUrSdna2hpubm6ltlZVqfo7ALK/hbxszKVFJBKhT58+kuzET548wb1799CwYUN4e3sL2vbv319t88bExGDBggW4ePFiicZR9TpT9R4jHXgt75xVRnH7FVdp3B8yMzOxatUq7Nu3D9nZ2SrNV5Cm75UlJS8wMTU1Fa9evcKNGzewZ88eQVD/nj17kJWVpfLz09fXF0uWLClxJntNf5/v378XlIODgxEcHFzicYvKLq4K6ezLgOobPgDysyKLxWJoaWkVd2llomrVqqhatSp69eoFAIiMjMSuXbvg6ekpc+3u3r0bo0aNQuXKlctiqUWqUqWKyn2MjIxgYWEheI+Wd47o6+tj5cqVmDhxIjIzMyX1T548wfr167F+/XoYGRmhQYMGaNasGVxdXdG8eXPo6uoW67NQ+SJ9DyrOPQOQvW+ocm8zMTFRaa6yfLcnIiIiIiIiIiIiIvrYqb5VORERERERERERERER0f8nLytqSYNEpbOkqpp5VZMBT9KBOGZmZmodX52BZdKUzXxuZGSksTUo4+rVqxg7dmyJA9sBzQeYfEzBdebm5vjyyy8l5aysLJns7PmkMwAPGjSoXAeOfUy/gyIDBgwQlI8dO4b09HScOXNGUlevXj04OjqqZb5Xr15hxIgRJQ5sBwCxWKxSe1XvMdJZsKWzpCqruP2KS9PnZWZmJqZNm4Zdu3aVKLAdUP03LA+MjIxQq1YtjBo1CidOnECPHj0Exz08PHD06FGlx/P29sa0adNKHNgOaP7Zo6l3BWXfE5QhvSmFtrZ2sa5B6UDTnJycTyIzcvXq1bFo0SLs3btXZiOMrKwsHDlypIxWVjRVg3/zSX9O6XMkX8uWLXHgwAHUq1dP7vHU1FQEBgZi06ZNcHd3R9u2bbFo0SJERUUVa11UfkifE8V9bkufa6rcMz+Fd0oiIiIiIiIiIiIioo8FM7cTEREREREREREREVGxyQtwSU1NLdGY0hlPixtEUxrUHQAhHdivTh9D8GJCQgJ++OEHSXbxfK6urujQoQPq16+PypUrw8rKCvr6+tDT0xO0++mnn2QyXdP/GTVqlCBgztPTE1OmTBFsIBEdHY3Lly9LyiKRCEOHDi3VdX6O6tSpg/r16+PBgwcAgBMnTqB+/fqCwG51Zm2fO3cuXr58KairUaMGevbsiUaNGsHW1hbW1tYwMDCAnp6e4Bzx8vLC3Llz1baWokhf58W9T2ry/loWtm7dikuXLgnqLC0t8eWXX6JZs2aoVq0abGxsYGRkBH19fUF22ZcvX8LNza20l6wxenp6+OOPPxATE4OQkBBJ/bJly9C2bVtUrFix0P7Pnz/HggULBEHpIpEI7du3R5s2bVCvXj3Y2NjA0tISenp6Mufk6NGjERgYqN4PVYhP7VxW1acUfNq0aVMsWbIE33//vaD+xo0bmD59ehmtSjNUeQ9t2LAhvL29cfnyZfz333+4du0aYmNj5bZNSEiAh4cHDh8+jO+++w6TJk1S15KpjKnrWv+U7hlERERERERERERERJ8SBrcTEREREREREREREVGxmZqaQltbWxAQJp1lV1XSGTnVnR29JCwsLARldWdPNTc3F5SrVq0KHx8ftc5Rnu3evRvx8fGSspmZGdavX4+WLVsq1b+kGyt86pycnNCkSRNJ8OerV6/g7++PTp06SdocOnRIcD136NABlStXLvW1fo769+8vCW6Pj4/HihUrJMd0dHTQp08ftcxz/fp13LhxQ1A3d+5cuLu7K9W/tK8z6WdAcZ8xn0K253wpKSnYtm2boK53795YunQpDA0Ni+z/Kd4r9fT08Ntvv6Ffv37IzMwEkJcFeO3atfj1118L7fv3339L+gBAlSpVsGnTJjg6Oio1t/SmPJom/a4wY8YMTJ06tVTXUBTp6zY3NxcpKSkqb1gkfd2KRKJiZ3Mur3r27IkVK1YgJiZGUhcZGamx+Qo+44ujuPdSVd/vtbS00L59e7Rv3x4A8PTpU9y8eRM3b95EcHCwzAYtWVlZWLVqFdLS0jBjxoxirfFTV9LfXtOkz4ninmvS7wnl6b8liYiIiIiIiIiIiIjo/2gX3YSIiIiIiIiIiIiIiEg+LS0tmYDvZ8+eFXu89PR0vHnzRlBnZWVV7PHUTXotL1680Oj4r1+/RnZ2tlrnKM+kA/nnzp2rdGA7AEFgPMk3YsQIQdnDw0Py56ysLBw+fFhwfNiwYaWyLsoLTtbV1ZWUExISJH9u164dKlSooJZ5pK+zAQMGKB3YDpT+dSaddTs6OloQiKysiIgIdS2pzF2+fBnp6emScvXq1bF8+XKlAtuBT/deWbNmTYwcOVJQ5+XlhefPnyvsk52dDT8/P0HdihUrlA5sB4TXammQfleIiooq1fmVIf1uCORdu6qSDmA2MzP75LIwa2lpoX79+oK6ws4p6c+vasBySTehevXqlcp9UlNTZT6TvHOkMA4ODhgyZAh+//13XLhwAadOncLEiRNhZGQkaLdly5ZP6n6fT1tb+M+7cnJyVB4jMTFRXcvRCOlzojj3DED2viG9IQgREREREREREREREZUPDG4nIiIiIiIiIiIiIqISkQ7Iefz4cbHHCg8PlwnSadCgQbHHUzfpz5qfAVtdHBwcoKenJylnZWXh9u3bap2jvMrOzsaTJ08kZR0dHfTq1Uvp/jk5OXj48KEmlvZJ6dGjhyBI+vLly5IgIB8fH7x//15yzM7ODu3atSv1NX6urKysFH7f/fv3V9s80vfovn37qtT/3r17aluLMhwcHATBi1lZWXj06JFKY7x9+xavX79W99LKjPRv2KNHD8Gzoyil/RuWpkmTJgnOl+zsbGzatElh+9evXwsCPitVqgRXV1el54uNjS12AGZxSQfeBwcHl+r8yrCysoK1tbWg7v79+yqPI92nbt26JVpXeSW9MYV0wHZB0pnrU1JSVJqrpOdrRESEYHMNZTx69Ejwfq+jo4NatWqVaB0ODg6YPXs2vLy8BJm5c3JycOrUqRKNXR5J/+6pqakq9ReLxTIbiJU3derUEZQTEhKKtXnH53LfICIiIiIiIiIiIiL62DG4nYiIiIiIiIiIiIiISqRx48aCckBAgMoBF/kuXLggKOvr66uUPVXTXFxcBOWHDx8KArJLysDAAE2bNhXUnTlzRm3ja5pIJBKUVckqGR8fD7FYLClbWlrCwMBA6f6BgYFITk5Wuv3HoiTfqTx6enoYPHiwpJybm4tDhw4BEGZxB4ChQ4fKZAolzRowYIBMnbm5OTp37qy2OWJjYwXlypUrK903OTkZQUFBaluLMkQiERo2bCioO3HihEpjqNq+vJP+DatUqaJSf+lM5Z8SKysrDBs2TFB3/PhxhQGSJbkegOJ9lyW9r7dp00ZQfvHiBR48eKDyOjStSZMmgrKPj49K/cVisUwf6TE/FdJBx1ZWVgrbFgzkBmSzVBelpPfw7OxsXLx4UaU+0u/3derUUekdrzA1atTA0KFDBXWFbbQlff1Jb6qlCTo6OoJycd7lTExMoKWlJSknJibiw4cPSvcPDQ1VOXO7ut9Bi1KzZk1YWloK6s6fP6/SGC9fvpTZ7Er6v62IiIiIiIiIiIiIiKh84L9GISIiIiIiIiIiIiKiEpEOukxLSytWIGFmZib+++8/QV2bNm1UykaraY0bN5YJfCssI2xxdO/eXVA+dOjQR5NxWDqrpCrB5rq6uoJySkqKSgFHO3bsULrtx6Qk36kiw4cPFwQsHTlyBI8fP0ZgYKCkTldXF4MGDSrxXKSajh07om/fvujVq5fkf99++61a74PS11pSUpLSfQ8cOFDszUtKok+fPoLykSNHEBMTo1TflJQU7Nq1SwOrKjvS54MqAYt37twpl5m+1Wn8+PHQ19eXlLOzs7F582a5baWvB1W+y5ycHOzevVvl9ZX0vl65cmU4OzsL6tatW6fyOjStQ4cOgvLly5fx4sULpfv7+fnJbErQsWNHdSytXImLi8Pdu3cFdfXr11fYvmbNmoLyrVu3lJ7rzp07CA0NVW2Bchw8eFDptikpKTLv9+r+He3s7ATlwp5TmnivKoo65hSJRKhWrZqgLiQkROn+qvxm+criu2rfvr2gfPDgQWRlZSndf9++fYLNsszMzD7ZTTGIiIiIiIiIiIiIiD52DG4nIiIiIiIiIiIiIqIScXJyQrNmzQR1q1evRlxcnErjbN68GdHR0YK6MWPGlHh96qSjo4Nx48YJ6k6cOCETtFMSgwYNQqVKlSTljIwMfP/998jIyCj2mAWDPDSpQoUKgvLTp0+V7mtubg5DQ0NJOTU1VRBsXZjDhw/j8uXLSs/1MSnJd6pIpUqV4ObmJim/f/8eM2fOFLTp3r17oZljSTP09PTwxx9/YPXq1ZL/jR49Wq1zFLy/AFA6A294eDj+/vtvta5FWb179xZkK05JScHcuXORmZlZaD+xWIxFixYpHQj/sbCxsRGU/f39leqXmpqKn376SRNLKlcqVqyIIUOGCOqOHTsm844ByF4PERERCrO8S9uwYQPCwsKKtT7pOVU1bdo0QfnixYvFCrTPp4n3hN69e8PCwkJSzs7OxqJFi5TauCY5ORnLli0T1DVs2BCNGzdW8ypLZt68eTh69GiJMlr/8ccfMsG7nTp1UtheemMDf39/vH//vsh5MjMzsXjx4uItUsr169dx6tQppdquW7cO7969k5RFIpHM9ZkvOzu7WOuRvoasra0VttXEe1VRjI2NBZnqk5OTi/Vckv7tDx8+rFS/O3fu4MiRIyrPp457lapGjRolKEdGRmLr1q1K9X348CH27t0rqBs8eLDguyciIiIiIiIiIiIiovKDwe1ERERERERERERERFRi06ZNg5aWlqQcFxeHMWPGyA0kkyYWi7Fjxw5s3LhRUN+sWTO0atVK7WstqSFDhqBGjRqCup9++gn79+9XKjhMLBbj/PnzCjPn6unpYfbs2YK6kJAQfP3113j58qXS68zJycGFCxcwevRoPHjwQOl+JeHk5CQoHzx4UOmAOS0tLbRo0UJQt3TpUnz48KHQft7e3li4cKFqC/2IlOQ7LcyIESMEZemApeHDh5d4DiqfXFxcBOV//vmnyHvE/fv3MXbsWKSnp2tyaQoZGhpi1qxZgrqrV69iwoQJCgOR379/jxkzZkg2HymYyftj5+rqKigHBQXh33//LbRPXFwcxo0bVyrBieXBhAkTBFnZs7KysGXLFpl2FSpUgIODg6QsFovxyy+/FLpxglgsxubNm2XeW5RVr149QTkwMBBPnjxRaYyOHTuibdu2groVK1Zg9erVKgUIx8fHY8uWLZgwYYJK8yvDwMAA48ePF9RdvXoVv/zyS6GZmBMTEzFp0iSZdx7pgP7y4Pnz5/jxxx/x5ZdfYu/evSpt7JSWlobFixfDy8tLUG9vb4+uXbsq7Ne8eXNBgHZ6ejrmzZtX6O+empqK7777Tq3vgz///DMCAgIKbbN7927s2rVLUNevXz9UrlxZbvuxY8di5cqVSv33Q7779+/D09NTUCd9jyxI+r3K09Oz2EH1ytLW1oajo6OgzsPDQ+VxunfvLij7+PjgxIkThfa5e/cupk6dqlL283zquFepytnZWebetn79ehw6dKjQfmFhYZg4caLgtzQ1NcXXX3+tkXUSEREREREREREREVHJ6ZT1AoiIiIiIiIiIiIiI6OPXpk0bjB07Fjt37pTUhYeHo2fPnhgyZAjc3NzQqFEjGBkZAcgLDIuOjsb169dx4MABPHz4UDCehYUF/vzzz1L9DMoyMDDA+vXrMWTIEKSmpgLICyRfsmQJjhw5ghEjRqBNmzaoVKmSJOA/ISEBjx49wtWrV3HmzBlERUVh+fLlaN68udw5+vTpgwcPHuCff/6R1IWEhKBnz57o06cPunfvjsaNG8Pc3FxyPDMzE8+ePUNoaChu3LgBX19fJCQkACi9zO2dOnXCyZMnJeVjx44hPDwcbdu2hbW1tSDQEMj7nCYmJpLysGHDcOnSJUk5PDwcAwYMwPTp09GpUydYWloCyMvaHBAQgP379+PKlSsA8gJX69ati7t372ryI5a6kn6nirRq1Qq1atWSG6RUu3Zthecmffz69++Pv//+G2lpaQDygh5HjhyJiRMnom/fvrC3tweQl0H37t27OHr0KI4cOSIJGHNxcUFgYGCpr3vYsGE4f/685JoHgICAAPTs2RMtW7aEs7MzLC0t8eHDBzx69AhXrlyRBOM7OjqiVq1agiDAghuyfGwaNmyI+vXrCwJVFyxYgNu3b2PkyJGoV68eRCIRxGIxIiIicO7cOfzzzz+SzULK6jcsTZUqVcLAgQMFQf9eXl6YOnWqTLb2YcOGCbKEBwQE4KuvvsK0adPQtm1byT31w4cPuHr1Knbu3Il79+4BACwtLVGhQgWVAj5r1qyJ6tWrIzIyEkBe4P3gwYPRpUsX1K5dGyYmJoLzs0aNGmjZsqXMOKtWrcKQIUPw/PlzAEBubi42b96M48ePY9iwYWjdujXq1q0reE4kJCQgLCwMDx8+xMWLFxEUFITs7GzUrl1b6fWrYvz48bh48SJu3rwpqfPy8sL9+/cxceJEdOzYEWZmZgCAt2/fwsfHB5s2bRJk+gaAoUOHFprNvKw9e/YMS5cuxe+//462bdvCxcUFTZo0gYODg+TzAXn32/DwcFy6dAmHDx/GmzdvBONoa2tj/vz5hW7GoauriyFDhmDTpk2SOj8/P4waNQrTp0+Hi4sL9PT0AADR0dHw8/PD9u3b8fr1awBAkyZNEBISUuzPWr9+fTx+/BhpaWlwd3fHsGHDMHjwYDg6OkJbWxuZmZkIDg7G7t27cfHiRUFfa2tr/PTTTwrHTkxMxI4dO7Bz5040bNgQbm5ucHZ2hqOjI6ysrCTtMjIy8PjxY5w6dQoeHh6CjVdsbGzQrVs3hXN06tRJkAk8ICAAX375JTp16oTKlStLvrt8nTt3ho2NjbJfT6Hz3r59W1LetGkTgoOD0aJFC1SoUAEikUjQXt4mQx07doSdnZ1g44f//e9/uHfvHoYOHYqaNWsCyHt+37t3T/L8zsrKgoWFBSwtLfHs2TOl16yue5WqfvvtN/Tt21fw3zHz58+Hr68vRo8ejRYtWkBPTw9isRhPnz7FsWPHsGvXLplNSRYtWqSW346IiIiIiIiIiIiIiDSDwe1ERERERERERERERKQWs2bNwrt373D8+HFJXUZGBvbu3Yu9e/cCyMu+q6+vj8TEROTm5sodx8LCAn///TeqVKlSKusujtq1a2Pjxo2YMWOGILP4gwcP8MsvvwAAdHR0YGJigrS0NGRkZKg8x5w5c5CdnS357oC8APYjR47gyJEjAPKyvBsbGyM1NbVYc6hb9+7d8ffffwsCZx4+fCizeUG+du3aCQKx3dzc0KlTJ/j5+UnqoqOjMXfuXACQtE1OTpYZa+HChQgKCvrkgttL+p0WZsSIEViyZIlMPbO2f9qsra3x7bffYuXKlZK6tLQ0rFu3DuvWrZPcpz98+CCzMcaAAQPKLDBaS0sL69evx+TJkwXzZ2Vl4fLly7h8+bLcfpUqVcLff/+N9evXC+o/5kzuWlpamDdvHsaMGSPIxuvl5QUvLy/o6urC2NgYycnJMhmJ69Spg19++QX9+vUr7WWXukmTJgk2ZsjKysLWrVuxYMECQbthw4bh6NGjgs0CwsLCMGPGDGhpacHU1BTZ2dmSDW3y6erq4s8//5SbEb4oU6ZMEQT5pqam4r///pPbdsCAAXIDRi0sLLBjxw5MnToVYWFhkvro6GisWrUKq1atAgAYGxtDR0cHycnJyMnJUXmtJSESibBmzRqMHz9esMawsDDMmTNHsr6cnBxBgHJB7du3x88//1wq6y2prKws+Pn5Cd5j8t8HMzMzZc6hgrS1tfHbb7+hQ4cORc4zZcoUnDlzRvBuEBISgvHjx0NbWxtmZmZISUmRydb91VdfoXnz5iUKbq9Tpw569+6N33//Hbm5uThw4AAOHDgAHR0dGBsbIzExUe6mSsbGxli3bp1gYyZFxGIx7t69K3iny/8ec3NzkZycLPe/I/T19fH777/D2NhY4dhNmzaVeY5FRkYKNpQqqGbNmmoJkB4yZAj27NmD2NhYSV1QUBCCgoLktpf3Lqajo4OlS5di7Nixku84JycHu3btwq5du6Cvrw8DAwOZ30BXVxerV6/Gpk2bVApuB9Rzr1KVjY0N/v77b3zzzTdITEyU1OdfW1paWpJzXPoZl2/atGno3bt3iddCRERERERERERERESao13WCyAiIiIiIiIiIiIiok9DfpDXTz/9JMnQLi0tLQ0JCQkKA9ubNGmCw4cPfxRZo1u1aoV///0XDRo0kHs8OzsbCQkJCoPOtbUL/2sakUiEefPm4c8//0SFChXktsnMzER8fHyhge1VqlSBhYVFoXOpi56eHjZu3FiiDLB//vknXF1d5R5LTk6WCWzX1dXF0qVL8dVXXxV7zvJMHd+pIv369ZMJADMyMvosgl4/d+PHj8e4cePkHsu/T0sHJw4dOhRLly4tjeUpZGRkhG3btmHixImCbNSKtGzZEocOHYKdnZ3MvcPU1FRTyywVTZs2xR9//AEDAwOZY1lZWUhISJAJ+mvSpAl27dql9AYYHzs7Ozv07dtXUOfp6YmYmBhBnZ6eHjZt2oS6devKjCEWi5GYmCgTlGxiYoINGzagbdu2xVrbgAED8O2338pka1aVvb09Dh06hEGDBikcKyUlBR8+fFAY2K6lpSX3s6vLF198gQMHDijMvJ6SkiI3sF1bWxsjRozApk2b5J7n5UGrVq0UvqPly38fLCywvU6dOti7dy8GDBig1LwGBgbYvn07qlWrJnMsNzcXCQkJMoHtI0eOxK+//qrU+EUZN26cZPOHfNnZ2XI3RQHyNlXZtm0bmjZtWui4BceTlv89Ktogq0qVKti5cydatWpV5Pr/+uuvIteiblZWVti4cSMqV65conFatWqF3377Te71npGRIfMbmJqaYtOmTWjdunWx5lPXvUpVzZs3x/79+yXZ6AsSi8X48OGD3MB2Y2NjLF26FN99911pLJOIiIiIiIiIiIiIiEqAmduJiIiIiIiIiIiIiEitxo4diwEDBmDfvn04deoUnj59Wmh7Y2NjuLi4YMyYMcUOvCgrNWrUwJEjR+Dj44M9e/YgJCREJpioIHNzc7Rp0wYDBgxAu3btlJqjT58+6Nq1Kzw9PeHt7Y1Hjx4p3Byg4Lpat26Nrl27omXLloUGC6lbzZo14eXlBV9fX/j6+iI0NBQxMTFyM4jKY2Jign/++Qf79u3Dzp078ebNG7ntdHV10a1bN0yfPl1u4MunpKTfqSImJiZo2rSpION17969P5vA18/djz/+iJYtW2LdunW4f/++wnbNmjXD1KlTix3Eq24GBgaYPXs2hg4diuPHj+PSpUuIjo5GfHw8dHV1UaVKFTRp0gS9e/cWZJAtmC0XgFLZg8u7nj17onbt2lizZg0uXLig8NlQrVo1fP311xg2bBhEIhFevnxZyistO5MnT8axY8ckgd2ZmZnYvn07fvnlF0E7GxsbHDp0CNu2bcO+ffuQkJAgdzwjIyP06dMH06ZNK3E25+nTp6NPnz7477//cOvWLURERCAxMRFpaWlyA4QVMTQ0xLJlyzB58mTs2LEDfn5+MgH80vT09NC4cWO0a9cOvXr1gp2dXYk+S1FMTU2xefNmXL9+HVu2bEFwcLDC55eRkRHatWuHqVOnwtHRUaPrKqmpU6diypQpuH37Nq5evYqbN2/izp07hQay5zMyMkKbNm3Qr18/dOrUCTo6qv3zHTs7Oxw+fBibN2+Gh4eHwjkbNGiA7777TqmM8KqYOnUqXFxcsHbtWkEW9ILMzc3Rt29fzJgxQ6kNRfbs2YNLly7h0qVLCA4ORnR0dJF9HB0d0b9/fwwfPlzpTRCsra2xf/9+XLlyBefOncPDhw/x6tUrpKSkIDMzU6kxiqNx48Y4deoUzpw5g0uXLuHx48d4//490tLSVHqfGzhwIGrXro2//voL169fl3u/0NXVRe/evfH999+Xm3uVqurUqYMTJ07g8OHDOHDgAEJDQxW2tba2Rs+ePTFlypQiN5wgIiIiIiIiIiIiIqLyQUusyb9pICIiIiIiIiIiIiKiz15cXBzu3r2L2NhYfPjwAZmZmTA1NYWFhQWqVq0KJyenUs8GqCmpqam4ffs2YmJiEBcXh6ysLBgZGcHa2hoODg5wcHAo8WdNSkrC7du38f79eyQkJCA9PR1GRkYwMzODvb09HBwcYGlpqaZPVLZyc3MRGhqKBw8eID4+Hrm5uTA1NUWNGjXQuHFjGBkZlfUSP2rx8fFo3769IJDLy8sL9evXL8NVUVmIioqS3FfS0tJgZGQEOzs7NGrUCNbW1mW9vBLLzs5G8+bNkZaWBiAvO3BQUNBHn729oISEBAQHB+PVq1dITk6Gvr4+bGxsUK9ePTg4OJT18j4qWVlZuH//PsLCwiRZkC0sLODg4ABnZ2fo6emV9RKLFBkZicePHyMhIQEJCQnQ0tKCsbExKlSogBo1aqBGjRpl+jlSUlJw69YtyfuSSCRChQoVUKVKFTRu3Pij+I4Vyc3NRXR0NCIjI/HmzRskJycjLS0NBgYGMDY2hqWlJWrXro1q1apBW1tbLXNmZmYiJCQEkZGRkt+7cuXKaNSoEapWraqWOQrz5s0bhISE4NWrV8jKykKFChVgZ2eH5s2bQ1dXt9jjxsbGIiIiAi9fvkRCQgLS0tKgp6cHExMT2NrawtHR8ZN4RpVEbGwsgoKC8PbtWyQnJ8PIyAg1atRAs2bNPrnNit6+fYu7d+9K/hvIyMgIVlZWcHBwgKOjY6lu5kVERERERERERERERCXH4HYiIiIiIiIiIiIiIiKiz9COHTuwcuVKSdnZ2Rmenp5luCIizfD398ekSZMk5Zo1a+L06dNluCIiIiIiIiIiIiIiIiIiIqLPl3q2gSYiIiIiIiIiIiIiIiKij0ZOTg48PDwEdSNHjiyj1RBpTm5uLrZs2SKoa926dRmthoiIiIiIiIiIiIiIiIiIiBjcTkRERERERERERERERPSZOXr0KKKioiTlChUqoFevXmW4IqKiZWZmqtznr7/+ws2bNwV1w4YNU9eSiIiIiIiIiIiIiIiIiIiISEUMbiciIiIiIiIiIiIiIiL6jDx79gwrV64U1Lm7u0NPT6+MVkSkHA8PD4wdOxbnz59Henp6oW2fPXuGb7/9Ftu2bRPUd+nSBbVr19bkMomIiIiIiIiIiIiIiIiIiKgQOmW9ACIiIiIiIiIiIiIiIiLSjJiYGPj6+gIAUlJS8OTJE5w8eVKQAdvGxgajR48uqyUSKU0sFuPatWu4du0aDA0N0ahRI9StWxcVK1aEsbExUlJS8PbtW9y+fRsPHjxAbm6uoL+1tTV+/fXXMlo9ERERERERERERERERERERAQxuJyIiIiIiIiIiIiIiIvpkRUZGYtGiRQqPa2lp4ddff4WhoWHpLYpIDdLS0nDjxg3cuHFDqfa2trbYvHkzrKysNLwyIiIiIiIiIiIiIiIiIiIiKox2WS+AiIiIiIiIiIiIiIiIiEqfjo4O5s+fjw4dOpT1UoiUUrlyZRgZGanUR09PD0OHDsXhw4dRp04dDa2MiIiIiIiIiIiIiIiIiIiIlMXM7URERERERERERERERESfCT09PVSuXBkuLi4YNWoUHB0dy3pJRErr3r07OnTogOvXryM4OBihoaF4+fIl4uLikJaWBgAwMzODhYUFHB0d0bx5c7i5ucHGxqaMV05ERERERERERERERERERET5tMRisbisF0FERERERERERERERERERERERERERERERERERERERESfNu2yXgARERERERERERERERERERERERERERERERERERERERF9+hjcTkRERERERERERERERERERERERERERERERERERERERBrH4HYiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiLSOAa3ExERERERERERERERERERERERERERERERERERERERkcYxuJ2IiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIg0jsHtREREREREREREREREREREREREREREREREREREREREpHE6Zb0AIiIiIiIiIiIiIiIiKp8yMzPx6NEjREZGIi4uDmlpadDT04O5uTns7Ozg5OQEc3Pzsl4mlVNeXl6YO3eupDxgwACsWLGiDFf06YuLi0NoaCiio6ORmJiIjIwMGBkZwdzcHBUqVED9+vVRoUKFsl4mEZUBVe/JL1++hJubm6Rsa2sLX19fja6xtAUEBGDMmDGSsouLC/bu3VuGK/q0JSYmIjQ0FC9fvkRCQgLS09NhaGgIMzMzWFlZoV69eqhUqVJZL5OIiIiIiIiIiIiIiIhKAYPbiYiIiIiIiIiIiIiISCI3Nxc+Pj7w9vbGtWvXkJGRobCttrY2nJyc0KdPHwwaNAgmJialuFIiAoDnz5/jyJEjOHfuHJ49e1Zke1tbW7Rt2xZ9+/ZFs2bNoKWlVQqrpLKyfv16bNiwQVI+duwYHB0dSzyudOAzAOzZsweurq4lHpuIPh1v377FkSNHcPbsWYSGhkIsFhfa3traGi1btkTfvn3Rpk0biESiUlopERERERERERERERERlSYGtxMREREREREREREREREA4Pr161iyZAkiIiKUap+bm4v79+/j/v372LhxI6ZNm4bRo0dDW1tbwyslTfPy8kJ0dLSkPGDAANjZ2ZXhikhaTEwMVq5ciVOnTiE3N1fpftHR0fj333/x77//onr16pgxYwZ69uz5yQe5JyYmYvfu3ZKyqakp3N3dy25BpeTChQuSP9va2qolsJ3y7Nq1C0lJSZLy119/DTMzszJc0efl/PnzePTokaTcpUsX1KtXrwxXRAV9+PAB69atw7///ousrCyl+7179w7Hjx/H8ePH8cUXX2Dq1KkYPHgwdHQ+/X/etH79ekH522+/LaOVEBERERERERERERERad6n/7c/REREREREREREREREVKjc3Fz8+eef2LFjR6HtzMzMkJKSgpycHJljHz58wG+//YYLFy5g7dq1sLS01NRyqRR4e3sjMDBQUnZxcWFwezly7tw5zJ07F8nJyYW2MzMzQ25uLlJTU+UGwEdGRuL777/HkSNHirz+P3aJiYmCDOa2traffHD7q1evBMG/nTt3LsPVfHr27NkjswkIg9tLz/nz5+Ht7S0p29raMri9nAgODsbMmTPx7t27QtsZGxtDJBIpfLd8+/YtFi1ahN27d+PMmTOaWm65UfAZBTC4nYiIiIiIiIiIiIiIPm0MbiciIiIiIiIiIiIiIvqM5eTkYM6cOTh58qTMsYYNG6JPnz7o2LEjKleuDD09PeTm5uL9+/cIDg7G6dOnceHCBUFAUkBAAEaMGIG9e/eiYsWKpflRiD4Lu3fvxm+//SZTb2pqiq5du6J9+/Zo2rQprKysoKurCwDIzMzE8+fPERwcjHPnzuHGjRuCYPdnz56V2vqp9BTM2g4Abm5uZbQSIvpcnDlzBrNnz5bJ1q6vr48uXbqgffv2aNGiBaytraGnpwcAyM7OxsuXL3Hr1i1cuHAB/v7+gv58RhEREREREREREREREX16GNxORERERERERERERET0GVu2bJlMYLu5uTl+/PFHfPXVVzLttbW18cUXX6BXr17o1asX7t69i19++QVhYWGSNhEREZg4cSI8PDxgYGCg8c9A5dPAgQMxcODAsl7GJ+XIkSMyge0ikQjDhg3D9OnTYWVlJbefnp4eateujdq1a2P48OGIjIzE33//jePHj0MsFpfG0qkMFAxuNzMzQ4sWLcpwNUTlj6urKx4/flzWy/hkXL16FT/88AOys7MF9b1798asWbNga2srt5+Ojg6qV6+O6tWrY+DAgYiJicG2bdvg4eEhMxYRERERERERERERERF9GrTLegFERERERERERERERERUNk6ePIn9+/cL6qysrODh4SE3sF0eZ2dnHDp0CM2aNRPUP3z4UG52aSIqnocPH2LhwoWCOl1dXaxZswYLFixQGNguT/Xq1fHHH39gz549qFy5srqXSuVAYmIigoODJeUOHTpAR4d73xORZrx58wYzZ84UBKNraWlh3rx5WLVqlcLAdnlsbGwwb948eHl5oU6dOppYLhEREREREREREREREZUxBrcTERERERERERERERF9hj58+IClS5cK6gwMDLBz5044ODioNJahoSG2bt2K2rVrC+oPHTokCK4kouLJzc3F3LlzkZWVJahft24dunXrVuxxXVxc4O3tjaZNm5Z0iVTO+Pv7C84XNze3MlwNEX3qFi1ahMTEREHdvHnzMHr06GKPWbduXXh6epboOUdERERERERERERERETlE4PbiYiIiIiIiIiIiIiIPkP//PMP4uLiBHVTpkxBvXr1ijWeiYkJlixZAi0tLUmdWCzGX3/9VaJ1EhHw33//ITQ0VFA3dOhQdO7cucRjW1paYuXKlSUeh8qXCxcuSP6sq6uLdu3aleFqiOhTFhwcDD8/P0Fd27ZtMWrUqBKPbWBggLVr15Z4HCIiIiIiIiIiIiIiIipfdMp6AURERERERERERERERFS6MjMz4eHhIaizt7fH+PHjSzRu06ZN0a9fPxw9elRSd/PmTdy9exfOzs7FHjc7Oxt37txBeHg4EhISYGBgABsbGzg7O8PW1rZEa5b28uVLPHr0CLGxsUhISICxsTEqVKgAR0dH1KxZU61z5YuPj8edO3cQFRWF5ORk6OrqolatWujYsWOh/ZKTk/H06VM8e/YMCQkJSEtLg7GxMczNzVGjRg04OTlBR+fT+uvAtLQ03Lp1C8+ePUNSUhJMTExgbW2N5s2bo2LFimqZIz4+Hjdv3kRMTAwSExNhYmKCatWqoWnTpjAxMVHLHKrauXOnoGxqaor//e9/ahtfW1v1PdFTUlIQEhKCmJgYxMXFQSQSwcrKCra2tmjUqBH09PRKvK6UlBQ8fvwYERERSEpKQlpaGvT19WFkZITKlSvD3t4eNWrUKNb61eXNmzcIDQ3Fq1evkJycjJycHBgaGsLc3By2traoWbOm2s5NZWVmZuLy5cuScsuWLcvs3FVVYmIibt68iefPnyMtLQ1mZmawsbGBi4sLzMzMSjR2VlYWnj59ivDwcMTHxyMlJQUikQhGRkawtraGnZ0datWqBX19fTV9GtWJxWJERUXh6dOnePXqFVJSUgAAFhYWqFChAho1alTq51NJpKen4+nTp4iIiEBcXBxSU1Ml14e9vT2cnZ3Vcq8oD6KiovDw4UPExsYiMTERpqamsLKyQt26dTX2/gAAoaGhePDgAWJjY6GtrQ0rKys4OjqiXr16gg2HNGnHjh2CskgkwqJFi9Q2fnHu8ZmZmQgJCcHr168RFxeH3NxcWFlZwcbGBk2bNoWhoWGJ15WRkYGwsDA8ffoUCQkJSE1Nha6uLoyMjGBjYwM7Ozs4ODhAV1e3xHMVV2xsLEJDQxEVFYWkpCRkZWXB0NAQpqamsLW1RfXq1VG5cuUyWx8REREREREREREREX2+Pq1/zUJERERERERERERERERF8vX1RUJCgqBuyJAhagkwGz58uCC4HQC8vb0LDW7v3LkzoqOjJeULFy7Azs4OaWlp2LJlCzw8PGTWm69x48b47rvv0KZNm2KvOTk5Gbt27cLx48cRGRmpsJ2dnR2GDh2KMWPGwMDAQKmxvby8MHfuXEl5wIABWLFiBQAgJCQEGzZswLVr15Cbmyvo5+joKDe4/e7duzhz5gxu3LiBR48eyfQryMjICJ07d8akSZNQt27dItc6evRoBAYGyj02ZsyYQvsuX74cAwcOFNQV9tnlCQgIEMzj4uKCvXv3AgDev3+P9evX4+jRo0hPT5fpq6WlBRcXF8yePbvYGyk8evQIf/75J27cuIHs7GyZ43p6eujVqxdmzpwpCQRTdO6q04MHD/D48WNBXd++fcssWPn69evYunUrgoKCkJWVJbeNkZER2rVrh2nTpil17kkLDg7Gzp07cenSJYVz5DM2NkaTJk3QrVs39OvXT3Btvnz5Em5ubnL7RUdHF7k26e89X1ZWFjw8PODp6YmwsLAiPg1ga2uL1q1bo2/fvnBxcSmyfUnduHEDycnJknKXLl00PqcyCrsnvHjxAmvWrMG5c+fk/uYikQidO3fGrFmzVA4Ujo6OxpYtW3DmzBl8+PCh0La6urqoV68eOnfujIEDB8LGxkZwXPqaL0jRuZZvz549cHV1lalPTEzEuXPn4O/vj8DAQIXPu3wODg4YNWoUvvrqqzINxFckPDwcp0+fxrVr13D//v1Cr2E9PT20adMGEyZMQPPmzYsc+6effoK3t7fcY3PnzhWcX9KmT5+Ob7/9VlBX2HNHGenp6di7dy+OHDmCZ8+eKWxnZ2eHfv36Ydy4cSrduxU9Y3Jzc+Hp6Ylt27YhKipKbl8bGxtMmTIFQ4YM0ehGN7GxsfD39xfUtWvXDvb29hqbszD379/Hpk2bcPXqVaSlpclto6enB1dXV0yZMkWp807a48ePsW3bNly4cAGpqamFtjUwMEDDhg3RpUsXDBgwAObm5oLjhT2HinpGKXrnEIvFOHbsGDw8PHD79u1CxwAAa2truLq6olevXkXex4iIiIiIiIiIiIiIiNSFwe1ERERERERERERERESfmYsXLwrK2tra6Nevn1rGbty4MWrWrImIiAhJnXTQkzJevHiBiRMnFhpsDgC3b9/GuHHjMGTIECxatAgikUileY4ePYrly5cXGUwI5AXKrlq1CgcOHMCGDRvQoEEDleYqaO3atdi0aRPEYrHSfb7//nucOnVK6fapqak4ceIETp48iSlTpmDGjBmllsVVna5fv46ZM2cW+huJxWIEBARg2LBhWLp0qUygfVH+/vtv/P3338jJyVHYJjMzE0ePHoWPjw/WrFmD9u3bqzRHcfn5+cnUDRo0qFTmLigpKQlz5syRux5pqampOHv2LHx8fDB8+HD8/PPPSgVX5uTkYMmSJTh48KDS60pJScGVK1dw5coVODs7o169ekr3LY4XL15gypQpePr0qdJ9oqOj4enpiXv37uHYsWMaXF2eCxcuSP6spaWFTp06aXzOkjhx4gR++eUXuRtX5MvJyYGPjw+uXLmC9evXo127dkqN7enpiaVLlxY6dkFZWVm4e/cu7t69C0NDQ7i7uyvVr7hCQ0MxaNCgIjdxKOjp06dYvHgxdu/ejY0bN8LBwUGDK1TNn3/+iW3btindPjMzE35+fvDz88NXX32FRYsWfTSZ3AMDAzFnzhy8efOmyLYvX77E33//DQ8PD/z2228luiYTEhIwY8YM3Lhxo9B2MTExWLx4Mfz9/bF27VqlN+VR1aVLl2SenWXxjMrMzMSiRYvg5eVV5LtVZmYmLl++jMuXL6N79+5YsWIFjIyMlJpHmfeFgtLT0xEUFISgoCDY2dlpfLORuLg4TJ06FSEhIUr3effuHU6cOAF/f38EBwdrcHVERERERERERERERET/R7usF0BERERERERERERERESlSzo7d61atWSy05ZEq1atBOXo6Gi8evVK6f5xcXFwd3eXCWw3NjZWmKX20KFD+N///qd0sJFYLMbq1avx448/yg2aFolEsLCwkBtk9/r1a4wePRrXr19Xai5p69atw8aNGwXBV9ra2jA3Ny80OD8xMVFuvZaWFkxMTBT2F4vF2LRpExYsWFCs9Zal69evY9KkSYLfSEtLC+bm5nJ/m5ycHPz8888q/TZ//fUX1q1bJ/fc0dXVhZmZmaAuJSUF06ZNw82bN5X/ICUgfb2amppqPIBb2tu3bzFixAiFge1GRkZyAydzc3Oxf/9+TJ06Vang4sWLFysMbNfV1YWFhQVMTEygrV02f80dHx+PkSNHKgxsNzIygqWlpcaCSJUhFosFv1PDhg3Ven9Xt6NHj2L27NmC8yP/fqirqyvTPi0tDVOnTlVqc4Hjx49j3rx5cs89kUgEMzMzWFhYyJ2ntKSnpysMbM8/5w0NDeUej4yMxJAhQ1TaaEHTFD2ngLzro7Dv+8iRI/jmm2+Qm5urqeWpzdmzZzF+/Hi5ge35zyh596m4uDhMmzYNnp6exZo3JSUFY8eOlQlsNzQ0VJgR/uLFi1i4cGGx5lOG9DMKAFq0aKGx+eRJTk7GhAkTcOTIEbmB7QYGBgqD18+ePYvRo0cjLi6uyHm2bNmi8H1BR0cH5ubmRb7LaVJmZia+/vprhYHthoaGsLS0VDqQn4iIiIiIiIiIiIiISJOYuZ2IiIiIiIiIiIiIiOgzkpSUhOjoaEFd/fr11TqHvPFCQ0NRpUoVpfovXbpUssbq1avjm2++QadOnWBubg4gL7j81KlT2LJlCz58+CDpd+LECTg6OmLixIlFzrFjxw5s3rxZUGdvb49Ro0ahXbt2qFmzpiTL+cuXL3H+/Hls374d7969A5CXmXrmzJk4duwYKlWqpNTnAoC7d+/i6NGjAAB9fX2MHDkSvXv3Rr169aCtrY2cnBxEREQUmjnTwcEBHTp0gIuLC2rXrg1bW1vJWnNzc/Hs2TNcvXoV+/fvF2wQcOjQIbi4uKBPnz5yx3V3d0evXr0AALt27RL0dXd3R/Xq1RWuqXHjxkp9flW8e/cOM2fORGZmJnR1dfHVV1+hX79+aNiwoSQ48smTJzh48CD2798vCYgUi8WYP38+zp49W2SA2fnz57FlyxZBnZGREcaPH48vv/wS1atXh5aWFjIzMxEYGIj9+/fD19cXmZmZmDNnjtLZoEsiNDRUUHZycpL83qUhJycHM2fORFhYmKDewcEBkydPRseOHSXXZkxMDHx8fLBp0ya8f/9e0tbf3x/Lli3Dr7/+qnCekJAQ/Pvvv4I6JycnfP3113B1dUWlSpUkn1ssFiM6OhphYWG4du0afH19Ze5rAGBhYYFFixYByMt2vGbNGsGxmTNnqvJVYPXq1Xj79q2krK2tjf79+6Nfv35o0KCBILg0IyMDT58+xYMHD3Dp0iVcvnxZpbmK6969e4iJiZGU3dzcSmXe4ggLC8PJkychFothaGiIUaNGoVevXnB0dIS2tjbEYjEePHiAf/75BydOnJD0y8zMxMKFC7Fv3z6FY6ekpGDp0qWCOmtra7i7u6Njx46oVq2aIMg6Li4O4eHhCAoKwsWLF3Hv3j25486cORMpKSkAgDVr1gg23pg5cyYsLCwUrqmwe6ihoSFatWqFDh06wMnJCQ4ODjA2NpYcT0xMxL179/Dff//h+PHjkuDa5ORkzJw5E0eOHClXGc9tbW3RsWNHtGzZEnXq1IG9vb3gfhwVFYUbN27Aw8MDDx48kNRfuXIFW7duxZQpU+SO279/fzRq1AhA3sYIt2/fFhwr7FnUoEGDkn2o/+/x48eYPXs2MjMzBfV9+/bF0KFD0bhxY+jo6CAnJwcPHjzA4cOH4enpKXlG5eTkYOHChahRowaaN2+u0twLFy7Ew4cPAQDOzs4YO3YsWrduLTnvPnz4AB8fH6xZs0byvgLkfVf9+/eX2XxIHR49eiQo29nZFXodaMLChQsREBAgqKtUqRKmTJmCLl26wNraGkDeBiV+fn7YtGkTXrx4IWl7//59zJkzB9u3b1f4fI2Ojsb69esFddWqVYO7uzvatm0LW1tbwTkeExODsLAwBAQEwM/PD0+ePJE7bv4zSvrP8srSpL/nf/75R+ZZ3bVrVwwePBiNGjUStM/KykJkZCQePXqES5cuwd/fv8iM90REREREREREREREROrE4HYiIiIiIiIiIiIiIqLPSMFgnnyOjo5qnUPeePLmVeTOnTsA8gJyVq1aJZOtvXLlyhg/fjz69OkDd3d3Qdba9evXo1u3bqhWrZrC8W/fvo3Vq1cL6kaOHImffvpJbnCgnZ0d3N3d0bdvX0ybNg23bt0CkBcsu3DhQpng6MLkr7VSpUrYuXMnHBwcBMdFIhFq166N2rVry/Tt2LEjpk+fjiZNmigcX1tbGw4ODnBwcMCwYcPw66+/4tChQ5Lj69atw5dffik3o2zBINhTp04Jgts7d+4MV1dXpT+nOjx79gwAULFiRWzatAnOzs4ybWrVqoV58+bByckJc+fOldRHRUXh4sWLhQb2JicnywSO2draYvfu3bC3txfU6+npoW3btmjbti0OHjyIRYsWyQ2mVreEhATBBg4AULduXY3PW9COHTtkstT369cPS5culblebGxsMGrUKPTp0weTJ08WZI89dOgQOnXqhM6dO8udJ3/Th3xdu3bFmjVroKMj+1faWlpasLOzg52dHTp37oxffvkFly5dQoUKFQTtTExMMHz4cAB5m1QUDG43NjaWHFNGZmYmTp48Kahbs2YNunfvLre9vr4+nJyc4OTkhMGDB+PDhw+4fv260vMV14ULFwTl8hzcnh/UXL16dWzbtg1Vq1YVHNfS0kKDBg2watUqVK9eHRs2bJAcCwoKQmhoqMLnl7+/vyDw3N7eHocOHYKVlZXc9lZWVnB1dYWrqyumT5+O0NBQmeBlIC+AOd+2bdsEc/Tp0wd2dnZFfu6CzMzMMHfuXAwaNEhh5u38dm3atEGbNm0wcuRITJo0CfHx8QD+b5OAAQMGqDS3JjRt2hTdunVD27ZtC21nb28Pe3t7fPXVV9i4caMgaHjbtm0YNWqU3O+jZcuWaNmyJYC8d4WCwe2urq4YOHCgej6IAtnZ2fjhhx8E54auri7Wrl0rc62JRCI4OzvD2dkZPXv2xDfffIO0tDQAeQHuc+bMwcmTJ1XKop1/T/32228xffp0mePm5uYYNGgQ2rRpg2HDhgkyy+/fv18jwe3S73el/Yw6efKkYPMLAGjTpg3WrVsncw5ZWlpi4MCB6NWrF2bPng0fHx/JsStXrmDfvn0YPXq0wnmysrIk5caNG+Off/5R+PvZ2NjAxsYG7dq1w+zZsxEcHAxLS0uZdgWfQ9LvJKo8owDZ5+iPP/6IcePGyW2rq6sred/s27cv0tLSBN8HERERERERERERERGRpsn+qxUiIiIiIiIiIiIiIiL6ZBXM5JlP3Rk25QXvFMx2rIx69erhr7/+kglsL+iLL77Ajh07ZLIl79ixo9CxV65ciezsbEl56NChWLBgQZFZb62srLBp0ybY2tpK6i5evIjHjx8X9XEEdHV1sWXLFpnA9qKMHj260MB2aXp6eliyZAlcXFwkdS9evCi1DNLqoKuri40bN8oNbC9o4MCB6Nixo6DuzJkzhfbx8vISXA96enrYtm2bTGC7tGHDhmHy5MmFL1xN5F03+VnSS0N6errM9dSyZUssX7680OvF3Nwc27ZtE1wrALBx40aFffKzEeebNWuW3MB2ebS0tNChQwd88cUXSrUvjqioKCQnJ0vKjRs3VhjYLo+5uTl69OihiaUJ+Pr6Sv5ctWpVuRtllCempqbYvn27TGC7tGnTpskEzRZ2jRfMBg4AEyZMUBjYLo+jo2OR9x11qFmzJtzd3QsNbJfm7Ows2KgByAtcLg/69+9fZGB7Qdra2pg+fbogMD85ORnHjh3TxPJK7Ny5cwgPDxfULVmypMhNJFq1aoU///xTUPfq1St4e3urvIbRo0fLDWwvqHLlyoINX4C895WMjAyV5ytMamoqUlJSBHWl+YwCZJ8rtWrVwt9//13oNWVgYIC//vpL5hrfunWrIIC9IOln1PTp01XamKB58+Yqv/epIiMjAxEREZLyF198AXd3d6X7GxoaCjbvICIiIiIiIiIiIiIi0jQGtxMREREREREREREREX1GpIOQgLzgQnWSN15qaqpKY8ybN6/IYHMgL4Br6tSpgrrjx48LglALCgkJEWShtrGxwU8//aT0uiwsLGSCyjw9PZXuD+QFRyvKNqxuWlpamDBhgqDuxo0bpTK3OgwaNAiNGjVSqu3QoUMF5fv37xfavmBGewAYM2aM0oFnU6dORaVKlZRqWxLyrhszMzONz5vv+PHjgszUOjo6WLx4MUQiUZF9TU1N8fPPPwvq7t27J8jmXlBiYqKgrGoGbE378OGDoFze1gfkBeCHhYVJyuU5a3u+yZMnF7mhBJAXBD148GBBXWHXeHk/n0qqZcuWgsDcBw8eKHzufQwmTpwoKAcEBJTRSgq3b98+QdnFxUXpbPFdunRBly5dBHV79uxRaX4LCwv88MMPSrXt2rUrKlSoIClnZWUhNDRUpfmKIu+dsjSfUdevX8eTJ08EdQsWLIChoWGRffX09LB48WJoaWlJ6t6+fYuzZ8/KbV/e7ykFn9UAYGtrC21t/pMwIiIiIiIiIiIiIiIqv/g3GURERERERERERERERJ8ReRkpVck8qQx5QUWZmZlK969duzaaN2+udPtBgwYJAuFTU1MRGBgot+2JEycE5a+++krlz9+tWzdBRmlFcykyZMgQldqXVOPGjQXlO3fulOr8JTFs2DCl2zZt2lRQjoyMRG5urty2MTExMtl3pYPjC6Ovr4/+/fsr3b645F2vygTtqculS5cE5Xbt2qF69epK93dzc5MJAPT395fbVnpTjKI2Jyht0gGbDx8+VHh+lZXz588LyuU9uF1ewHphpK/xglmKpZX380kdCm78kZubi3v37pXhakrGwcFBkGm7PD6nkpKSZDbnGDVqlEpjjBkzRlCOjIzEixcvlO7fr18/pZ8BIpFIJjN5YddMcZT1M0r6eVKnTh24uroq3d/JyQktWrQodMx85f2eIr2+iIgIlTeWIiIiIiIiIiIiIiIiKk06RTchIiIiIiIiIiIiIiKiT4Wurq5MnbqDX9LS0mTqlMnCnk/VgExzc3M0b94c165dk9TduXMHnTt3lmkrHYjetm1bleYCABMTE1SrVg1Pnz4FAISHhyMlJQXGxsZF9rW0tESdOnVUnlORtLQ0hIeH4927d0hJSUFaWlqRAbevX79W2/yaZGZmhrp16yrd3sLCAqampkhKSgKQF+yZkpIiE/AFALdv3xaUq1evjqpVq6q0vnbt2mHz5s0q9VGVvOtV3vWlKdKBnF27dlWpv5aWFrp164adO3cqHDOfs7OzIDh37ty5WLt2LRwdHVWaU1Nq1KghOL8iIiIwf/58zJ07VxCUW5YuXLgg+bOlpaVMMHh5U6dOHVhYWCjdXjrDe/5vIY90UO+WLVtQvXp19OjRQ6U1lpXo6GhERkYiKSkJycnJcoOIo6KiBOVXr16V1vJUkpmZiYiICLx+/RopKSlITU1FTk6OTLuCm8bExMQgNze3XGWevn37tuD5qquri06dOqk0houLCywtLREfHy+pu3XrltLPHxcXF5Xmk75mpLOPl9TH/owCgO7duwveDQt7Rp05c0ZSXr58Ob744guVguk1ycjICLVr15Zs3PPhwwfMmjULy5YtQ4UKFcp4dURERERERERERERERLIY3E5ERERERERERERERPQZkZelvLAAweKQN54q2dGdnJxUntPJyUkQ3P748WOZNqmpqTLZum/duoWwsDCV5yuYiT43NxexsbFKBberI7A9JiYGR44cwenTp/HkyROVs0erO7hNU6pUqQItLS2V+hgbGwvOv+TkZLnB7dLZa4sTQF2vXj1oaWlBLBar3FdZpXG9KhIXF4d3794J6ho0aKDyONJ95F2bADBkyBAcOHBA8n1GRkaif//+cHV1Rbdu3dCqVSvUrFlT5fnVRSQSYfDgwYJA/cOHD+PMmTPo0aMHOnXqhBYtWsDc3LxM1hcfH49bt25Jyp06dYJIJCqTtSjL1tZWpfbS99jk5GSFbTt16gQbGxvExMQAyLv/z5gxA7Vq1ULPnj3Rvn17ODk5CQKqy5JYLIafnx+OHz+OS5cuFfrZFCmte4MyEhIScPToUZw6dQoPHjxAdna2Sv3FYjGSkpLK7HqSR/reVadOHZU27gHyNvyoX78+rly5onDcwmjymimOsnxGAbLfnTqeUVFRUUhNTZX5bP369cP69eslwfuxsbEYM2YMnJ2d0aNHD7Rp0wZ16tQp0w0Zhg0bhl9//VVS9vPzQ6dOndC1a1d07twZrq6uqFixYpmtj4iIiIiIiIiIiIiIqKDy8Te1REREREREREREREREVCqsra1l6hISEtQ6h7zxvvjiC6X7V6lSReU5pfvIW0NsbKxMIPKff/6p8lzyJCQkKJV5VZUsxdLEYjG2bt2KTZs2lSgzakpKSrH7liZ5QelFkQ7mlZcdGJAN8Jd3XRTF2NgYhoaGSE1NVbmvsuSt68OHDxqbryB515CqgZUAYGdnJygnJiZCLBbLbFzg6OiI77//Hn/99ZekTiwW48aNG7hx4wYAwMrKCo0bN0aLFi3QsmXLYm2EURLffvstAgIC8ODBA0ldcnIyDh8+jMOHD0NLSwsODg5o0qQJXFxc0Lp161ILJLx48aLgfHdzcyuVeUtC1Wtc+voubGMPfX19rFy5EhMnThRsRvLkyROsX78e69evh5GRERo0aIBmzZrB1dUVzZs3l5uJWtOePn2KX375RWHGaGWpO3C5uA4fPow//vijxO8WKSkp5Sq4XfreW5z7ISB7T1Tlnm5iYqLSXKpcM8VhbGwMY2NjwXtFaT2jMjMzZd6F1PGMAvI+g3Rwe8WKFbFkyRL8+OOPgu/x7t27uHv3LgDAzMwMzs7OaN68OVxdXdG4ceNSDXYfPnw4/P39cenSJUldRkYGTpw4gRMnTgAAqlatiiZNmqBFixZo3bp1sc9jIiIiIiIiIiIiIiKikmJwOxERERERERERERER0WfE3t5epi40NFStc8gbT968iqgavAXIBknKC67SZMBVenq6Uu1UyWAvbd68eTh8+HCx++fTZKZxdVI1a7sqpDPLSme3VZaJiYlGg9stLS1hZmYmCMZXJctvSUhvAKCtrV2s70n6es7JyUFycrLcwObJkyejcuXK+P333/H+/XuZ43FxcfD19YWvry+AvCC9r776CqNGjSrWfUNVRkZG2Lt3L1asWIEjR47IbJ4gFovx5MkTPHnyBJ6enhCJRHB1dcWYMWPQqVMnja7twoULkj/r6+ujTZs2Gp1PHTR5jQNAy5YtceDAAcyfPx+PHj2SOZ6amorAwEAEBgZi06ZNsLCwQM+ePTF+/HiVnlkl8ejRI7i7u6tlk5nycG/fuHEj1q5dq5ax1B2IXVLS7xDFveco876iiKavmeKwt7cXvPeV1jNK3vemjvfH/LErV64sU9+3b19YWlpiyZIlePHihczxxMREXLlyBVeuXAGQt7FTv379MHbsWFSoUEHltalKJBJh48aNWL9+PXbt2oWMjAyZNi9evMCLFy9w7NgxAEDjxo0xYsQI9O7dW2YzBCIiIiIiIiIiIiIiIk1icDsREREREREREREREdFnxNzcHLa2toiOjpbUFcxCrA7yxnN0dFTrHNKUCerLysoq0/lL4ujRozKB7UZGRujZsydcXFxQs2ZN2NjYwMTEBPr6+tDREf41YN26dTW6vo+Nnp6eoFzcc0OT51Q+R0dHBAYGSsoPHjyQm/n8Y1LY2vv27YuuXbvi1KlTOHXqFG7duqVwA4EXL15g9erV2L17N1asWIEOHTpoaskSxsbG+PXXXzFhwgR4eXnB19cX4eHhcu8BOTk5uHbtGq5du4bWrVtj5cqVsLa2VvuaMjIycPXqVUm5devWMDQ0VPs8H6OGDRvC29sbly9fxn///Ydr164hNjZWbtuEhAR4eHjg8OHD+O677zBp0iSNri0rKwuzZs2SCWxv0KABunTpgoYNG6Jy5cqwtraGvr4+9PT0BNfO+vXrsWHDBo2uURVBQUEyge16enro2rUrXF1dUbduXdjY2MDU1BT6+vrQ1dUVtO3cubPg3eRz8THfywHAyclJENweFRWFhIQEWFhYlPpaivNdqtqnXbt2OHXqFM6fP4+TJ08iICBAZjOYfG/fvsW2bduwf/9+zJ8/HwMHDlR5farS1dXFrFmzMHLkSBw7dgw+Pj548OCBzGYs+W7fvo3bt29j165dWL16NapXr67xNRIREREREREREREREQEMbiciIiIiIiIiIiIiIvrsNGvWTBBA9uTJE8TExMDGxkYt41+/fl1QtrW1ha2trdL9k5OTVZ5Tuo+5ublMG+k6XV1d3L17F9ra2irPV5rEYrFMwGDLli2xZs0aWFpaFtk/JSVFU0v7aElnai3OOVeSfqpo0aKFILg9KSkJjx49gpOTk0bnNTMzE5Rzc3ORkpKicmZc6e9IJBIVmQHe0NAQX331Fb766itkZWXh4cOHCA4Oxs2bN3Hz5k2ZYOC4uDhMnToVW7ZsQdu2bVVaX3FVq1YN33//Pb7//nskJCQgODgYt27dwq1bt3Dv3j1kZ2cL2l+7dg1jx47FwYMH1Z5l/tq1a4INANzc3NQ6/sdOS0sL7du3R/v27QEAT58+lZxLwcHBePnypaB9VlYWVq1ahbS0NMyYMUNj6zp27BgiIiIkZV1dXaxcuRK9evVSqr+iTR/Kypo1awTlunXrYtOmTUo//8v7s0r6HaK49/+kpCRBWfpe+7Fp3rw5vLy8BHVBQUHo2rWrRueV954n/d0qQ15guryxC9LV1UXPnj3Rs2dP5Obm4vHjx5J7SlBQEN69eydon5qairlz5yI3NxeDBg1SeY3FYWNjg0mTJmHSpElITk5GSEgIbt68iVu3biEkJASZmZmC9g8fPsTo0aPh6emJSpUqlcoaiYiIiIiIiIiIiIjo81a+/6UOERERERERERERERERqV2nTp0E5dzcXBw7dkwtY9++fRtPnz4V1OUHFCrr1atXKs8r3UdexlArKytBOSsrC2/evFF5rtJ2//59weczMzPDunXrlApsB4D4+HhNLe2jJZ09+9mzZyqPERUVVSqZ26WvVwA4cuSIxueVdw0VJ6uydOCwmZmZSplydXV10ahRI4wfPx4bN27EtWvXsG/fPvTu3VswTnZ2NhYuXCgTVF4aLCws0KVLF/zvf//DwYMHcf36dSxfvhx16tQRtAsPD8f27dvVPv+FCxckf9bW1kbnzp3VPsenxMHBAUOGDMHvv/+OCxcu4NSpU5g4cSKMjIwE7bZs2SIIPlc3Hx8fQXny5MlKB7YD5eveHhsbi1u3bknKIpEIGzZsUDqwPTs7u1iByaVJ+p5Y3Czz0vfEogKpy7sOHTpAJBIJ6krjGaWnpydzzarjGQWo9ptoa2ujXr16GDVqFFavXo3Lly/jyJEjGD58OHR1dQVtly9fLrM5S2kwMTFBu3btMHPmTOzZswcBAQFYs2YNmjRpImj39u1brFq1qtTXR0REREREREREREREnycGtxMREREREREREREREX1m3NzcZDKFenp6ymRxLA4PDw+ZugEDBqg0xsOHD1WeV7pP3bp1ZdpYWFigSpUqgrqgoCCV5yptjx8/FpQ7dOigUuDVvXv31L2kj16DBg0E5YcPH6ocqH7nzh11Lkmhhg0bygRJ//fffxrPGm9lZSWzCcD9+/dVHke6j7xrUxUikQgtWrTAqlWrsHr1asGxly9fCgJsy4qZmRkGDhwIb29vmUDz//77T61z5ebmws/PT1Ju1KgRKlSooNY5PnUODg6YPXs2vLy8BM/GnJwcnDp1SmPzSt/b+/btq1L/8nRvDwsLQ25urqTcqFEjVK1aVen+Dx8+RE5OjiaWpjbS9+GwsDCV35vEYrFS7ysfk4oVK8psYnTp0iW5QePqJv2bqOMZZW9vLxM0rwotLS00aNAAixYtwp49ewQB7snJyYL7dVkxMjJCz549cfDgQYwcOVJw7Ny5c8jIyCijlRERERERERERERER0eeEwe1ERERERERERERERESfGX19fQwbNkxQ9+LFC+zYsaNE4966dUsmA3yTJk3QqFEjlcbx9fVVqf2HDx8QHBwsqHN2dpbbtlWrVoLy6dOnVZqrLMTFxQnK0gH6RSlOIJV0FtaCQYufAicnJ+jr60vKycnJ8Pf3V2mMEydOqHtZCo0dO1ZQTkxMxMqVK9U2vqLfVzqrq3Sm6aKIxWKZPtJjlkTPnj1l7i/SAcP5dHR0BOXSCKTV0dHB7NmzBXXR0dFq3Zjg9u3beP/+vaTcpUsXtY39ualRowaGDh0qqFN0PgElv0/GxsYKypUrV1a674sXL/D06VOV5tOk8vCc0vQ13bhxY2hr/98/scnKysLFixdVGiMoKEjmu2ratKk6llempJ9ROTk5WLhwodrG19QzCgDOnj1b6Jgl0bRpU3Tt2lVQp8o9pTSeU7NmzRIE4KenpyMyMlLj8xIRERERERERERERETG4nYiIiIiIiIiIiIiI6DM0btw4WFhYCOo2b96MR48eFWu85ORkLFiwAGKxWFA/a9YslccKCwuTCVYvzOHDhwXZU42MjODq6iq3bffu3QVlPz8/3L17V+U1lqaCQUdAXmCzsl6/fl2szMPGxsaCsqazhJc2PT09dOvWTVC3efNmpYNT79+/r3IwfEn069dPJkPtv//+q/JGEPIkJCTgxx9/lHusQ4cOgvLly5fx4sULpcf28/NDVFSUoK5jx44qr7EwdnZ2gnJaWprcdmV1Ttvb28vUKVpjcVy4cEFQdnNzU9vYnyPp8yk1NVVh25KeU9L39qSkJKX77tixQ+Z5W5ZK8pxKTk7GwYMHVZ5T+vtPSUlReQxVmJqaygSi79u3T6Ux9u7dKyjXqFFDpQz35ZWrq6tM9vYrV66o/P3Ik56ejhkzZsg9Jv2MCgsLQ2BgoNJjh4aGIigoSFCn6WeUJu8pxWFiYiLz3wPqfEYREREREREREREREREpwuB2IiIiIiIiIiIiIiKiz5ClpSXmzp0rqEtPT8e4ceNUzgablpaGSZMmITw8XFA/aNAguLi4FGt9S5cuFQSsK/LmzRts3LhRUNe7d2+YmJjIbd+hQwc0bNhQUDd79mzEx8cXa50ANB5gaGNjIyhfuXJFqWyeOTk5+N///oesrCyV56xQoYKgXJ4yBKvLiBEjBOV79+5h/fr1RfZLSEjA3LlzSzWbvUgkwm+//SYTQPrdd9/h3LlzxR43ODgYAwcOxM2bN+Ue7927tyDoLTs7G4sWLVLqsycnJ2PZsmWCuoYNG6Jx48YybcVicbG/z4iICEG5YsWKctsZGxvDwMBAsL6YmBil58nOzlbL+kQiEaysrIo1ljwFg9tr1qyJGjVqqG3sj5m6fi9ra2uFbUt6n6xUqZKgrGwW8OvXr+Pff/9VaS5Nk/4sN2/eVDowd8mSJTLZzJUhfa2XxnNq1KhRgnJAQACOHj2qVF8/Pz+Z+/Xo0aPVtbQyt3jxYpiamgrqli5dKhPQr4rw8HAMGTJE4XOuVatWqF27tqBuyZIlSE9PL3LsrKwsLFy4UPAO98UXX8hsfJOvvN9Tiru++Ph4metP0XOUiIiIiIiIiIiIiIhInRjcTkRERERERERERERE9Jnq378/Bg8eLKiLi4vDiBEj4O3trdQY9+7dw9ChQ2WCYx0dHTFv3rxir+3Ro0eYNWsWMjIyFLZ5+/Ytxo0bJwig09PTw7hx4wod+8cff4SOjo6k/Pz5c4wYMQKhoaFKr08sFuPGjRv45ptvcP78eaX7FYeLiwu0tLQk5aioKKxdu7bQPqmpqfj2229VymBakJOTk6B89OjRQrONfoyaNm2KXr16Ceo2btyIX3/9VWFQ5oMHDzB69GiEhYVBS0tLJthckxo2bIgFCxYI6rKysjBz5kz8+uuvKgWHRkVFYe7cuRg1ahSio6MVtjMwMMD48eMFdVevXsUvv/xS6KYJiYmJmDRpEl6+fCmonzZtmtz2SUlJ6NatG/bs2aNSptqDBw/i0aNHkrKWlhZatGght622tjYcHR0FdR4eHkrPdeDAAUyaNAnXrl1TekOL9PR0LF++XFDXrFkziEQipectTEREBJ49eyYpM2v7/xk7dixWrlxZ6Pkt7f79+/D09BTUubq6KmwvfZ/09PRUKcBUevOX1atXF7ney5cvY+rUqeUqazuQ910U3FQmJSWlyI0w8jfLOHbsWLHmrFevnqDs4+OD9+/fF2ssZXXt2lUmmHr+/PlFbkwQEBCAWbNmCeqqVKmCAQMGqHuJZaZKlSr466+/BPc3sViMpUuX4ocfflDpWnz//j1WrFiBAQMG4PHjx4W2/eabbwTl8PBwTJ8+vdB3loyMDPzwww+4ffu2oH7y5MkKn+t9+vTBxo0bERsbq9yHAODv7w8/Pz9BnSr3lIMHDyp9rV+8eBEjRoyAj4+P0vehnJwc/Pbbb4INk+zs7GBra6tUfyIiIiIiIiIiIiIiopLQKboJERERERERERERERERfaoWLVqEDx8+CLJiJiQk4KeffsL+/fvRt29fdOzYEZUqVYKenh5yc3MRFxeHoKAgnDp1ChcuXJDJIl69enVs27YNhoaGxVpTo0aNcOfOHfj4+KBv376YOnUqOnXqBDMzMwB52dpPnTqFzZs348OHD4K+06dPLzJzcYsWLfDTTz9h6dKlkrqIiAgMHDgQXbp0QZ8+fdC0aVNBBs2srCxERUUhNDQUwcHBOH/+vCTrc79+/Yr1OZVVsWJFdOnSBT4+PpK6LVu2IDw8HOPHj0ejRo0kwVjR0dG4cOECtm/fLllfixYtEBQUpNKcHTp0gLa2tiQw8dmzZ+jZsyfc3NxQtWpV6OvrC9q7urqiZs2aJfmYZWL+/Pm4efOmIIP3vn37cOzYMXTo0AG1atWCsbExYmNjERgYiNu3b0u+k+HDh8Pf318QsFdwEwJNGDJkCJKTk/H7779L6nJyciRr7tatG9q3b48mTZrAyspKcl5kZWXh+fPnuHXrFnx8fHD16lWZ61aR8ePH4+LFi4INLLy8vHD//n1MnDgRHTt2lFybb9++hY+PDzZt2oR3794Jxhk6dCg6deqkcJ6oqCgsW7YMK1euRJs2bdC+fXs0aNBA8hvkS0pKwu3bt+Hp6YmzZ88KxujcuTPs7e0VztGpUydBMOOmTZsQHByMFi1aoEKFCjJB58OHD5f8OTc3F/7+/vD394e1tTW6du2KFi1awMnJCXZ2dpINM8RiMaKjo3HlyhX8888/iIyMFIz59ddfK1yfqgpmbQcY3F5QYmIiduzYgZ07d6Jhw4Zwc3ODs7MzHB0dYWVlJWmXkZGBx48f49SpU/Dw8BBkfLaxsVGYxRnIO5+2bt0qKQcEBODLL79Ep06dULlyZejp6Qnad+7cGTY2NpLysGHDBMGr7969w8CBAzFt2jR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    " ] @@ -4205,517 +4244,196 @@ "execution_count": 10, "metadata": {}, "outputs": [ + { + "data": { + "text/plain": [ + "alts_probs\n", + "ec 0.104173\n", + "er 0.051373\n", + "gc 0.517023\n", + "gr 0.240261\n", + "hp 0.087170\n", + "Name: p, dtype: float64" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "idata_m1[\"posterior\"][\"p\"].mean(dim=[\"chain\", \"draw\", \"obs\"]).to_dataframe()['p']" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
    " + ] + }, + "metadata": { + "image/png": { + "height": 1011, + "width": 2011 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(1, 2, figsize=(20, 10))\n", + "ax = axs[0]\n", + "counts = wide_heating_df.groupby(\"depvar\")[\"idcase\"].count()\n", + "predicted_shares = idata_m1[\"posterior\"][\"p\"].mean(dim=[\"chain\", \"draw\", \"obs\"])\n", + "ci_lb = idata_m1[\"posterior\"][\"p\"].quantile(0.025, dim=[\"chain\", \"draw\", \"obs\"])\n", + "ci_ub = idata_m1[\"posterior\"][\"p\"].quantile(0.975, dim=[\"chain\", \"draw\", \"obs\"])\n", + "ax.scatter(ci_lb, [\"ec\", \"er\", \"gc\", \"gr\", \"hp\"], color=\"k\", s=2)\n", + "ax.scatter(ci_ub, [\"ec\", \"er\", \"gc\", \"gr\", \"hp\"], color=\"k\", s=2)\n", + "ax.scatter(\n", + " counts / counts.sum(),\n", + " [\"ec\", \"er\", \"gc\", \"gr\", \"hp\"],\n", + " label=\"Observed Shares\",\n", + " color=\"red\",\n", + " s=100,\n", + ")\n", + "ax.hlines(\n", + " [\"ec\", \"er\", \"gc\", \"gr\", \"hp\"], ci_lb, ci_ub, label=\"Predicted 95% Interval\", color=\"black\"\n", + ")\n", + "ax.legend()\n", + "ax.set_title(\"Observed V Predicted Shares\")\n", + "az.plot_ppc(idata_m1, ax=axs[1])\n", + "axs[1].set_title(\"Posterior Predictive Checks\")\n", + "ax.set_xlabel(\"Shares\")\n", + "ax.set_ylabel(\"Heating System\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see here that the model is fairly inadequate, and fails quite dramatically to recapture the posterior predictive distribution. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Improved Model: Adding Alternative Specific Intercepts\n", + "\n", + "We can address some of the issues with the prior model specification by adding intercept terms for each of the unique alternatives `gr, gc, ec, er`. These terms will absorb some of the error seen in the last model by allowing us to control some of the heterogenity of utility measures across products. " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling: [alpha, beta_ic, beta_oc, y_cat]\n", + "Compiling...\n", + "Compilation time = 0:00:02.168994\n", + "Sampling...\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "2d00909ee14a443bad05112fa666925e", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/2000 [00:00\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "
    <xarray.DataArray 'p' (alts_probs: 5)>\n",
    -       "array([0.08414602, 0.13748865, 0.26918857, 0.38213088, 0.12704589])\n",
    -       "Coordinates:\n",
    -       "  * alts_probs  (alts_probs) <U2 'ec' 'er' 'gc' 'gr' 'hp'
    " + "\n" ], "text/plain": [ - "\n", - "array([0.08414602, 0.13748865, 0.26918857, 0.38213088, 0.12704589])\n", - "Coordinates:\n", - " * alts_probs (alts_probs) " - ] - }, - "metadata": { - "image/png": { - "height": 1011, - "width": 2011 - } - }, - "output_type": "display_data" - } - ], - "source": [ - "fig, axs = plt.subplots(1, 2, figsize=(20, 10))\n", - "ax = axs[0]\n", - "counts = wide_heating_df.groupby(\"depvar\")[\"idcase\"].count()\n", - "predicted_shares = idata_m1[\"posterior\"][\"p\"].mean(dim=[\"chain\", \"draw\", \"obs\"])\n", - "ci_lb = idata_m1[\"posterior\"][\"p\"].quantile(0.025, dim=[\"chain\", \"draw\", \"obs\"])\n", - "ci_ub = idata_m1[\"posterior\"][\"p\"].quantile(0.975, dim=[\"chain\", \"draw\", \"obs\"])\n", - "ax.scatter(ci_lb, [\"ec\", \"er\", \"gc\", \"gr\", \"hp\"], color=\"k\", s=2)\n", - "ax.scatter(ci_ub, [\"ec\", \"er\", \"gc\", \"gr\", \"hp\"], color=\"k\", s=2)\n", - "ax.scatter(\n", - " counts / counts.sum(),\n", - " [\"ec\", \"er\", \"gc\", \"gr\", \"hp\"],\n", - " label=\"Observed Shares\",\n", - " color=\"red\",\n", - " s=100,\n", - ")\n", - "ax.hlines(\n", - " [\"ec\", \"er\", \"gc\", \"gr\", \"hp\"], ci_lb, ci_ub, label=\"Predicted 95% Interval\", color=\"black\"\n", - ")\n", - "ax.legend()\n", - "ax.set_title(\"Observed V Predicted Shares\")\n", - "az.plot_ppc(idata_m1, ax=axs[1])\n", - "axs[1].set_title(\"Posterior Predictive Checks\")\n", - "ax.set_xlabel(\"Shares\")\n", - "ax.set_ylabel(\"Heating System\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can see here that the model is fairly inadequate, and fails quite dramatically to recapture the posterior predictive distribution. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Improved Model: Adding Alternative Specific Intercepts\n", - "\n", - "We can address some of the issues with the prior model specification by adding intercept terms for each of the unique alternatives `gr, gc, ec, er`. These terms will absorb some of the error seen in the last model by allowing us to control some of the heterogenity of utility measures across products. " - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Sampling: [alpha, beta_ic, beta_oc, y_cat]\n", - "/Users/nathanielforde/mambaforge/envs/pymc_examples_new/lib/python3.9/site-packages/pymc/sampling/mcmc.py:243: UserWarning: Use of external NUTS sampler is still experimental\n", - " warnings.warn(\"Use of external NUTS sampler is still experimental\", UserWarning)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Compiling...\n", - "Compilation time = 0:00:01.339706\n", - "Sampling...\n" - ] - }, - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "6943d65a34a249e5b398c009bbe60029", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - " 0%| | 0/2000 [00:00" ] }, "metadata": {}, @@ -4723,125 +4441,118 @@ }, { "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "0d1ed424e08147209b25eaf2f95e177e", - "version_major": 2, - "version_minor": 0 - }, + "text/html": [ + "\n", + "
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    \n", " beta_ic\n", + " -0.002\n", " 0.001\n", - " 0.000\n", - " -0.000\n", - " 0.001\n", + " -0.003\n", + " -0.001\n", " 0.000\n", " 0.000\n", - " 1215.0\n", - " 1612.0\n", - " 1.00\n", + " 2607.0\n", + " 2813.0\n", + " 1.0\n", "
    \n", "
    \n", " beta_oc\n", - " -0.003\n", + " -0.006\n", " 0.001\n", - " -0.005\n", - " -0.001\n", + " -0.008\n", + " -0.003\n", " 0.000\n", " 0.000\n", - " 1379.0\n", - " 1743.0\n", - " 1.00\n", + " 1259.0\n", + " 1520.0\n", + " 1.0\n", "
    \n", "
    \n", " alpha[ec]\n", - " 1.039\n", - " 0.497\n", - " 0.076\n", - " 1.936\n", - " 0.016\n", - " 0.012\n", - " 908.0\n", - " 1054.0\n", - " 1.00\n", + " 1.179\n", + " 0.379\n", + " 0.491\n", + " 1.900\n", + " 0.011\n", + " 0.008\n", + " 1291.0\n", + " 1583.0\n", + " 1.0\n", "
    \n", "
    \n", " alpha[er]\n", - " 1.077\n", - " 0.474\n", - " 0.216\n", - " 1.988\n", - " 0.016\n", - " 0.012\n", - " 839.0\n", - " 991.0\n", - " 1.00\n", + " 1.481\n", + " 0.310\n", + " 0.913\n", + " 2.080\n", + " 0.009\n", + " 0.006\n", + " 1271.0\n", + " 1607.0\n", + " 1.0\n", "
    \n", "
    \n", " alpha[gc]\n", - " 2.376\n", - " 0.309\n", - " 1.789\n", - " 2.953\n", - " 0.011\n", - " 0.008\n", - " 814.0\n", - " 836.0\n", - " 1.01\n", + " 1.602\n", + " 0.211\n", + " 1.184\n", + " 1.989\n", + " 0.005\n", + " 0.004\n", + " 1467.0\n", + " 1402.0\n", + " 1.0\n", "
    \n", "
    \n", " alpha[gr]\n", - " 0.733\n", - " 0.373\n", - " -0.031\n", - " 1.374\n", - " 0.013\n", - " 0.009\n", - " 854.0\n", - " 947.0\n", - " 1.01\n", + " 0.266\n", + " 0.191\n", + " -0.085\n", + " 0.634\n", + " 0.005\n", + " 0.004\n", + " 1379.0\n", + " 1507.0\n", + " 1.0\n", "
    \n", "
    \n", "\n", @@ -5003,20 +4714,20 @@ ], "text/plain": [ " mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk \\\n", - "beta_ic 0.001 0.000 -0.000 0.001 0.000 0.000 1215.0 \n", - "beta_oc -0.003 0.001 -0.005 -0.001 0.000 0.000 1379.0 \n", - "alpha[ec] 1.039 0.497 0.076 1.936 0.016 0.012 908.0 \n", - "alpha[er] 1.077 0.474 0.216 1.988 0.016 0.012 839.0 \n", - "alpha[gc] 2.376 0.309 1.789 2.953 0.011 0.008 814.0 \n", - "alpha[gr] 0.733 0.373 -0.031 1.374 0.013 0.009 854.0 \n", + "beta_ic -0.002 0.001 -0.003 -0.001 0.000 0.000 2607.0 \n", + "beta_oc -0.006 0.001 -0.008 -0.003 0.000 0.000 1259.0 \n", + "alpha[ec] 1.179 0.379 0.491 1.900 0.011 0.008 1291.0 \n", + "alpha[er] 1.481 0.310 0.913 2.080 0.009 0.006 1271.0 \n", + "alpha[gc] 1.602 0.211 1.184 1.989 0.005 0.004 1467.0 \n", + "alpha[gr] 0.266 0.191 -0.085 0.634 0.005 0.004 1379.0 \n", "\n", " ess_tail r_hat \n", - "beta_ic 1612.0 1.00 \n", - "beta_oc 1743.0 1.00 \n", - "alpha[ec] 1054.0 1.00 \n", - "alpha[er] 991.0 1.00 \n", - "alpha[gc] 836.0 1.01 \n", - "alpha[gr] 947.0 1.01 " + "beta_ic 2813.0 1.0 \n", + "beta_oc 1520.0 1.0 \n", + "alpha[ec] 1583.0 1.0 \n", + "alpha[er] 1607.0 1.0 \n", + "alpha[gc] 1402.0 1.0 \n", + "alpha[gr] 1507.0 1.0 " ] }, "execution_count": 13, @@ -5037,12 +4748,12 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 15, "metadata": {}, "outputs": [ { "data": { - "image/png": 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HHx4HHXRQdOzYMZo1axbVq1eP5cuXx9dffx2ffPJJvPzyy5GXlxcRPzS/3nbbbVG/fv3o1atXSnKAiizT6nvFihVJD4d988038eWXX0ZERHZ2dvTp0yd69+4dbdu2jaysrJg+fXq8+eab8fe//z3WrVsXERGjR4+Om2++Of74xz9ucx5QGWRafZfU+vXr45133kk6dsopp6T9ukDFVlE/8wAAIFXuuOOOmDFjRiLeZZdd4qKLLiq/hAAquK09O1SlSpXo27dvXHTRRdG8efMyzAyg4svPz49bb701cV/40ksvjTZt2pRvUgBERMQ///nPOO200+KBBx6IQw89tLzT4f/T3F6B/fjw+o9ycnJKdf7GO7ltPF9FzwcqMvUElVdFru+PPvooHnvssUSclZUV//u//xsNGzYssxwgk1Xk+t7Qu+++G++//36cdNJJccstt0SdOnXKJQ/IJJla36+++mqMHDkyIiIaNGgQ119/fUrmhe1Jptb3lVdeGXvttVexTScNGzaMHj16RI8ePeLCCy+Mq6++OvFZUFhYGP369YuuXbtGgwYNUpILVFSZVt8bN6b9uIt7tWrV4oknnogDDjgg6f3dd989dt999zjiiCPi0ksvjTVr1kRExAcffBBDhgyJww8//CflAxVZptV3SX366aexcOHCRNy1a9do3bp1mVwbqLgq6mceAACkwl//+td44403EnFubm7cf//9FmwCSKPCwsLo379/DBgwIH7+85/HNddcs8nPFwAo3mOPPRbffPNNRETsvPPOcfHFF5dzRgCVW7NmzeKII46I/fffPzp27BiNGjWK3NzcWLp0aUycODE++uijeOONNyI/Pz8ifnhW56qrror+/fvHXnvtVc7ZE6G5vULb+Ad0BQUFpTr/x8Lc3HwVPR+oyNQTVF4Vtb4///zzuPbaa5N2mbviiis8TA8bqAj1Xa1atZg8eXIiXrduXSxbtiymTJkSH3/8cbz22muxatWqKCwsjDfffDMmTZoUL7zwQtSrVy/luUBFkon1vXDhwrjvvvsS8Y033qiRFbZBJtZ3RET37t1LNK5x48bx5JNPxtlnnx0TJkyIiIi8vLx46qmn4oYbbkhJLlBRZVp9b+783/zmN5s0tm+oZ8+ecc0118Tdd9+dOPbMM8/4/zjbtUyr75La8GH8CLu2AyVTUT/zAADgp/rggw/i3nvvTTp25513xu67715OGQFUDm3btk16dig/Pz/R/PPBBx/EO++8EwUFBVFQUBDPPfdcTJkyJf785z9rcAfYismTJ8czzzyTiO+44w6fnQBp9L//+7/RrVu3yM7etD26SZMm0aRJkzj44IPjwgsvjCuuuCKmTJkSET8sBH311VfHBx984HM6A1Qp7wTYdjVr1kyKS7vK+sbja9WqlVH5bDwfbE8yrb6B1KmI9T158uSkXeIiIs4666y44oor0n5tqEgqYn1nZ2dHo0aNomfPnnHLLbfEO++8E506dUq8P2nSpLjzzjvTngdkukys77vuuiuWL18eET80wWqMgW2TifVdWjVq1Ijbb7896dj7779f5nlApsm0+i7u59316tWLvn37bvXcs846Kxo2bJiIP//881i6dOlPygcqskyr75JYvnx5DBkyJBHXqFEjjjnmmLRfF6j4KuJnHgAA/FTDhw+P66+/PgoLCxPHrr32WvfDANIgNzc3mjZtGoccckjcc8898eqrr8YOO+yQeP/f//53PProo+WYIUDmKywsjFtvvTWxOOkpp5wSPXr0KOesACq3nj17FtvYvrGddtopnn/++WjRokXi2Jw5c+KVV15JZ3qUkOb2CmzjG9krV64s1fkbjs/Ozv7Jq7RvfCP8p+RT3HywPcm0+gZSp6LV97fffhsXXnhhonkuIuK4446L2267La3XhYqootV3cXbcccd45plnknZqf/fdd+Prr78u81wgk2RafX/88ccxaNCgiIjIycmJO+644yfNB9uzTKvvbdWlS5do165dIp47d27MmDGjXHKBTJFp9V29evVNbqrtv//+JZo3Nzc3DjzwwERcVFQUY8aM+Un5QEWWafVdEu+9915Sg+lRRx0VtWvXTvt1gYqvIn7mAQDAT/Hll1/Gr371q8jPz08cu/DCC+OXv/xlOWYFsP3o1KlTPPXUU5GTk5M49te//jWWLFlSjlkBZLb+/fvHF198ERER9evXjxtuuKGcMwJgQ40aNYrrrrsu6ZjNYzKD5vYKrFmzZknx/PnzS3xuUVFR0viN5yrrfCIi5s2bl3j94w6SsL3KtPoGUqci1ff8+fPj/PPPj4ULFyaOHXTQQXHfffdFlSr+GQkbq0j1vSWNGzfeZPfIDz/8sJyygcyQafV97733Jl7/8pe/jF122eUnzwnbq0yr75+iS5cuSfF3331XPolAhsjE+t54nvbt25f43A4dOiTFpf35O1QmmVjfW/Pmm28mxXaaA0qqIn7mAQDAtpoyZUpcfPHFsWrVqsSx008/XXMQQBlr3759HHfccYl4zZo1MWzYsHLMCCBzrVmzJv7whz8k4htuuCEaNmxYfgkBUKyjjz46aQH6sWPHxurVq8sxIyIisrc+hEzVtm3bpHjOnDklPvf777+PgoKCRJyKB+FbtmwZ1atXjzVr1pQ6n6KioqTm9tatWyet+Abbm0yrbyB1Kkp9L168OC644IKk/Lp27RqPPvqov6NhMypKfZfEAQccEI8//nginjx5cjlmA+Uv0+p7wxXR//znP8ef//znUp0/cuTI2G233RJxt27d4q9//etPzgsqokyr759i44Ui7Z7A9i4T67tt27ZJedSrV6/E5248dtmyZSnJCSqiTKzvLZk+fXqMHTs2Ebdo0SL222+/tF8XqBwq2mceAABsq2+//TZ+8YtfxNKlSxPHjjnmmLjzzjvLLymA7dj+++8fb731ViL27BBA8fLz85MWZ7r11lvj1ltv3eI5RUVFSfGbb74Zb7/9diLu3bt33H333alNFGA7l52dHXvssUcMHz48IiLWrVsXCxYsiJ122qmcM9u+2XKzAmvatGnUqVMnEU+cOLHE506YMCEpTsWN7CpVqkSbNm0S8bfffhsrV64s0bnTpk2LtWvXpjQfqMgyrb6B1KkI9Z2XlxcXXXRRTJs2LXGsc+fO8Ze//CWqV6+elmtCZVAR6rukNm6Oy8vLK6dMIDNkcn2vX7++RL+2dF5hYWFKc4KKJJPru7Q2Xkm2WrVq5ZQJZIZMrO927dolxfn5+SU+d+OxapztWSbW95ZsvGv7ySefHFlZWWm/LlA5VLTPPAAA2Bbz58+P888/PxYuXJg4dsghh8QDDzwQVap4zBmgPDRu3Dgp9uwQQMmU5DmujZ/VKioq8iwXQBmweUzm8VOfCm7fffdNvF60aFF8++23JTpv9OjRSXG3bt1Sns/69evjyy+/LNF5Y8aMSUs+UJFlWn0DqZPJ9b1mzZq45JJLYvz48Ylj7dq1i6effjpq166d8utBZZPJ9V0aG9+Qqlu3bjllApmjstQ3sKnKUt+zZs1Kihs2bFhOmUDmyLT67t69e1I8f/78Ep87b968pLhBgwYpyQkqqkyr780pLCxM2mkjIuKUU05J6zWByqeifOYBAMC2WLx4cZx//vkxZ86cxLHu3bvHn/70p8jJySnHzAC2b54dAgCgsrF5TObR3F7BHXHEEUnxBx98UKLzBg0alHhdrVq1OOCAA8o1n43HbTwPbI8yrb6B1MnU+i4oKIirrroqRo0alTjWunXrePbZZzXGQAllan2X1sa7Ou2www7llAlkjkyq71GjRsXkyZNL/Ovjjz9OOr979+5J7/fv3/8n5wQVWSbV97ZavXp1fPbZZ4k4Ozs72rdvX275QKbItPo+4IADombNmol444azLdl4gdjddtstJTlBRZVp9b05w4cPj7lz5ybifffdN3baaae0XhOofCrKZx4AAJRWXl5eXHTRRTF9+vTEsT333DOeeOKJqF69ejlmBoBnhwBKpm7duqV6jmvy5MnxwgsvJM1xyimnJL1/7733ltNXA1C52Twm82hur+AOP/zwpNUpX3nllSgoKNjiOcOHD49vvvkmER9yyCFJD9T9FN27d08q7Pfeey+WL1++xXNmzpwZ//nPfxJx586do1WrVinJByqyTKtvIHUysb4LCwvjxhtvjGHDhiWONW/ePJ577rlo1qxZyq4DlV0m1ndpFRUVxauvvpp0bP/99y+nbCBzVIb6BopXGer7r3/9a9LuCXvttVfUqVOn3PKBTJFp9Z2bmxtHHnlkIv7yyy9jypQpWz1v2rRp8fnnnyfipk2bWsCC7V6m1ffmvPHGG0mxXduBbVFRPvMAAKA01qxZE5deemmMHz8+caxDhw7x9NNPR+3atcsxMwDWrFkT77zzTtIxzw4BAFCRzZ07N77++utE3KhRo2jatGk5ZkSE5vYKr3HjxnHGGWck4m+//TaefPLJzY5fu3Zt/O53v0vEWVlZcdlll212/OzZs6Njx46JX4cffvgW88nJyYmLLrooEa9YsWKLqwYVFhbG7bffHoWFhYljv/rVr7Z4DdheZFp9A6mTifX929/+Nt57771E3KhRo3juuedixx133Oq5wP/JtPr+8ssvS5H9D/74xz8mnbfDDjtEjx49Sj0PVDaZVt9A6mRafU+ePLkU2Ud8+umn8eijjyYdO//880s1B1RWmVbfET/8/Ds7OzsR//a3v91ic9q6devit7/9bRQVFSWOnXPOOVu9DlR2mVjfG8vLy4uPPvooEdeoUSOOPfbYUs8DkO7PPAAAKGvr1q2LX//61/HZZ58ljrVp0yaee+65qFevXjlmBlC55Ofnx6RJk0p1zo/P9n/33XeJY3vttVfssssuqU4PAADKzOOPP5707M0BBxwQWVlZ5ZgREZrbK4VLLrkkatWqlYgfeeSReO6555IaxiMiFi9eHBdddFFMnTo1cey4446L3XbbLaX59O3bN3bYYYdE/Np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    " ] @@ -12960,9 +12671,9 @@ ], "metadata": { "kernelspec": { - "display_name": "pymc_examples_new", + "display_name": "Python 3 (ipykernel)", "language": "python", - "name": "pymc_examples_new" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -12974,7 +12685,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.16" + "version": "3.11.6" }, "myst": { "substitutions": { @@ -12983,5 +12694,5 @@ } }, "nbformat": 4, - "nbformat_minor": 2 + "nbformat_minor": 4 } From 154a503ead1375f2f7f68598bd28cdd5524cc151 Mon Sep 17 00:00:00 2001 From: mitch-at-orika Date: Sat, 9 Dec 2023 09:36:14 +1000 Subject: [PATCH 2/2] precommit hooks --- .../GLM-discrete-choice_models.ipynb | 10 +++++++--- .../GLM-discrete-choice_models.myst.md | 18 +++++++++++------- 2 files changed, 18 insertions(+), 10 deletions(-) diff --git a/examples/generalized_linear_models/GLM-discrete-choice_models.ipynb b/examples/generalized_linear_models/GLM-discrete-choice_models.ipynb index f94ea942d..2d2e2edf9 100644 --- a/examples/generalized_linear_models/GLM-discrete-choice_models.ipynb +++ b/examples/generalized_linear_models/GLM-discrete-choice_models.ipynb @@ -599,7 +599,9 @@ " u1 = beta_ic * wide_heating_df[\"ic.er\"] + beta_oc * wide_heating_df[\"oc.er\"]\n", " u2 = beta_ic * wide_heating_df[\"ic.gc\"] + beta_oc * wide_heating_df[\"oc.gc\"]\n", " u3 = beta_ic * wide_heating_df[\"ic.gr\"] + beta_oc * wide_heating_df[\"oc.gr\"]\n", - " u4 = beta_ic * wide_heating_df[\"ic.hp\"] + beta_oc * wide_heating_df[\"oc.hp\"]#np.zeros(N) # Outside Good\n", + " u4 = (\n", + " beta_ic * wide_heating_df[\"ic.hp\"] + beta_oc * wide_heating_df[\"oc.hp\"]\n", + " ) # np.zeros(N) # Outside Good\n", " s = pm.math.stack([u0, u1, u2, u3, u4]).T\n", "\n", " ## Apply Softmax Transform\n", @@ -4262,7 +4264,7 @@ } ], "source": [ - "idata_m1[\"posterior\"][\"p\"].mean(dim=[\"chain\", \"draw\", \"obs\"]).to_dataframe()['p']" + "idata_m1[\"posterior\"][\"p\"].mean(dim=[\"chain\", \"draw\", \"obs\"]).to_dataframe()[\"p\"]" ] }, { @@ -4579,7 +4581,9 @@ " u1 = alphas[1] + beta_ic * wide_heating_df[\"ic.er\"] + beta_oc * wide_heating_df[\"oc.er\"]\n", " u2 = alphas[2] + beta_ic * wide_heating_df[\"ic.gc\"] + beta_oc * wide_heating_df[\"oc.gc\"]\n", " u3 = alphas[3] + beta_ic * wide_heating_df[\"ic.gr\"] + beta_oc * wide_heating_df[\"oc.gr\"]\n", - " u4 = 0 + beta_ic * wide_heating_df[\"ic.hp\"] + beta_oc * wide_heating_df[\"oc.hp\"] # Make one constant zero\n", + " u4 = (\n", + " 0 + beta_ic * wide_heating_df[\"ic.hp\"] + beta_oc * wide_heating_df[\"oc.hp\"]\n", + " ) # Make one constant zero\n", " s = pm.math.stack([u0, u1, u2, u3, u4]).T\n", "\n", " ## Apply Softmax Transform\n", diff --git a/examples/generalized_linear_models/GLM-discrete-choice_models.myst.md b/examples/generalized_linear_models/GLM-discrete-choice_models.myst.md index 18f089a66..f2defacb2 100644 --- a/examples/generalized_linear_models/GLM-discrete-choice_models.myst.md +++ b/examples/generalized_linear_models/GLM-discrete-choice_models.myst.md @@ -5,9 +5,9 @@ jupytext: format_name: myst format_version: 0.13 kernelspec: - display_name: pymc_examples_new + display_name: Python 3 (ipykernel) language: python - name: pymc_examples_new + name: python3 myst: substitutions: extra_dependencies: jax, jaxlib, numpyro @@ -98,14 +98,14 @@ This assumption proves to be mathematically convenient because the difference be $$ \text{softmax}(u)_{j} = \frac{\exp(u_{j})}{\sum_{q=1}^{J}\exp(u_{q})} $$ -The model then assumes that decision maker chooses the option that maximises their subjective utility. The individual utility functions can be richly parameterised. The model is identified just when the utility measures of the alternatives are benchmarked against the fixed utility of the "outside good." The last quantity is fixed at 0. +The model then assumes that decision maker chooses the option that maximises their subjective utility. The individual utility functions can be richly parameterised. When contants are included, one alternative's constant must be fixed at 0 in order to normalise the overall level of the constants. $$\begin{pmatrix} u_{gc} \\ u_{gr} \\ u_{ec} \\ u_{er} \\ -0 \\ +u_{hp} \\ \end{pmatrix} $$ @@ -150,7 +150,9 @@ with pm.Model(coords=coords) as model_1: u1 = beta_ic * wide_heating_df["ic.er"] + beta_oc * wide_heating_df["oc.er"] u2 = beta_ic * wide_heating_df["ic.gc"] + beta_oc * wide_heating_df["oc.gc"] u3 = beta_ic * wide_heating_df["ic.gr"] + beta_oc * wide_heating_df["oc.gr"] - u4 = np.zeros(N) # Outside Good + u4 = ( + beta_ic * wide_heating_df["ic.hp"] + beta_oc * wide_heating_df["oc.hp"] + ) # np.zeros(N) # Outside Good s = pm.math.stack([u0, u1, u2, u3, u4]).T ## Apply Softmax Transform @@ -215,7 +217,7 @@ which suggests that there is almost twice the value accorded to the a unit reduc To assess overall model adequacy we can rely on the posterior predictive checks to see if the model can recover an approximation to the data generating process. ```{code-cell} ipython3 -idata_m1["posterior"]["p"].mean(dim=["chain", "draw", "obs"]) +idata_m1["posterior"]["p"].mean(dim=["chain", "draw", "obs"]).to_dataframe()["p"] ``` ```{code-cell} ipython3 @@ -272,7 +274,9 @@ with pm.Model(coords=coords) as model_2: u1 = alphas[1] + beta_ic * wide_heating_df["ic.er"] + beta_oc * wide_heating_df["oc.er"] u2 = alphas[2] + beta_ic * wide_heating_df["ic.gc"] + beta_oc * wide_heating_df["oc.gc"] u3 = alphas[3] + beta_ic * wide_heating_df["ic.gr"] + beta_oc * wide_heating_df["oc.gr"] - u4 = np.zeros(N) # Outside Good + u4 = ( + 0 + beta_ic * wide_heating_df["ic.hp"] + beta_oc * wide_heating_df["oc.hp"] + ) # Make one constant zero s = pm.math.stack([u0, u1, u2, u3, u4]).T ## Apply Softmax Transform