Bayesian Statistics the Fun Way

8THE PRIOR, LIKELIHOOD, AND POSTERIOR OF BAYES’ THEOREM

Now that we’ve covered how to derive Bayes’ theorem using spatial reasoning, let’s examine how we can use Bayes’ theorem as a probability tool to logically reason about uncertainty. In this chapter, we’ll use it to calculate and quantify how likely our belief is, given our data. To do so, we’ll use the three parts of the theorem—the posterior probability, likelihood, and prior probability—all of which will come up frequently in your adventures with Bayesian statistics and probability.

The Three Parts

Bayes’ theorem allows us to quantify exactly how much our observed data changes our beliefs. ...