Bayesian probability allows us to systematically update our understanding (in a probabilistic sense) of a situation by considering data. In more technical language, we update the prior distribution (our current understanding) using data to obtain a posterior distribution. This is particularly useful, for example, when examining the proportion of users who go on to buy a product after viewing a website. We start with our prior belief distribution. For this we will use the beta distribution, which models the probability of success given numbers of successes (completed purchases) against failures (no purchases). For this recipe, we will assume that our prior belief is that we expect 25 successes from 100 views (75 fails). This means that our prior belief follows a beta (25, 75) distribution. Let's say that we wish to calculate the probability that the true rate of success is at least 33%.
Our method is roughly divided...
