Streamline introductory tutorial

The excised material is more appropriate for the very first page that
people click on.

Author: penelopeysm

Diff for: tutorials/00-introduction/index.qmd

@@ -1,5 +1,5 @@
 ---
-title: Introduction to Turing
+title: "Introduction: Coin Flipping"
 engine: julia
 aliases: 
   - ../
@@ -12,23 +12,12 @@ using Pkg;
 Pkg.instantiate();
 ```
 
-### Introduction
+This is the first of a series of guided tutorials on the Turing language.
+In this tutorial, we will use Bayesian inference to estimate the probability that a coin flip will result in heads, given a series of observations.
 
-This is the first of a series of tutorials on the universal probabilistic programming language **Turing**.
+### Setup
 
-Turing is a probabilistic programming system written entirely in Julia. It has an intuitive modelling syntax and supports a wide range of sampling-based inference algorithms.
-
-Familiarity with Julia is assumed throughout this tutorial. If you are new to Julia, [Learning Julia](https://julialang.org/learning/) is a good starting point.
-
-For users new to Bayesian machine learning, please consider more thorough introductions to the field such as [Pattern Recognition and Machine Learning](https://www.springer.com/us/book/9780387310732). This tutorial tries to provide an intuition for Bayesian inference and gives a simple example on how to use Turing. Note that this is not a comprehensive introduction to Bayesian machine learning.
-
-### Coin Flipping Without Turing
-
-The following example illustrates the effect of updating our beliefs with every piece of new evidence we observe.
-
-Assume that we are unsure about the probability of heads in a coin flip. To get an intuitive understanding of what "updating our beliefs" is, we will visualize the probability of heads in a coin flip after each observed evidence.
-
-First, let us load some packages that we need to simulate a coin flip
+First, let us load some packages that we need to simulate a coin flip:
 
 ```{julia}
 using Distributions
@@ -43,8 +32,7 @@ and to visualize our results.
 using StatsPlots
 ```
 
-Note that Turing is not loaded here — we do not use it in this example. If you are already familiar with posterior updates, you can proceed to the next step.
-
+Note that Turing is not loaded here — we do not use it in this example.
 Next, we configure the data generating model. Let us set the true probability that a coin flip turns up heads
 
 ```{julia}
@@ -63,13 +51,20 @@ We simulate `N` coin flips by drawing N random samples from the Bernoulli distri
 data = rand(Bernoulli(p_true), N);
 ```
 
-Here is what the first five coin flips look like:
+Here are the first five coin flips:
 
 ```{julia}
 data[1:5]
 ```
 
-Next, we specify a prior belief about the distribution of heads and tails in a coin toss. Here we choose a [Beta](https://en.wikipedia.org/wiki/Beta_distribution) distribution as prior distribution for the probability of heads. Before any coin flip is observed, we assume a uniform distribution $\operatorname{U}(0, 1) = \operatorname{Beta}(1, 1)$ of the probability of heads. I.e., every probability is equally likely initially.
+
+### Coin Flipping Without Turing
+
+The following example illustrates the effect of updating our beliefs with every piece of new evidence we observe.
+
+Assume that we are unsure about the probability of heads in a coin flip. To get an intuitive understanding of what "updating our beliefs" is, we will visualize the probability of heads in a coin flip after each observed evidence.
+
+We begin by specifying a prior belief about the distribution of heads and tails in a coin toss. Here we choose a [Beta](https://en.wikipedia.org/wiki/Beta_distribution) distribution as prior distribution for the probability of heads. Before any coin flip is observed, we assume a uniform distribution $\operatorname{U}(0, 1) = \operatorname{Beta}(1, 1)$ of the probability of heads. I.e., every probability is equally likely initially.
 
 ```{julia}
 prior_belief = Beta(1, 1);