Diving into Bayesian analysis

Welcome to the first section on Bayesian analysis. This section discusses the basic concepts used in Bayesian statistics. This branch of statistics often involves classical statistics and requires more knowledge of mathematics and probability, but it seems to be popular in computer science. This section will get you up to speed with what you need to know to understand and perform Bayesian statistics.

All Bayesian statistics are based on Bayes' theorem; in Bayesian statistics, we consider an event or parameter as a random variable. For example, suppose that we're talking about a parameter; we give a prior distribution to the parameter, and a likelihood of observing a certain outcome given the value of the parameter. Bayes' theorem lets us compute the posterior distribution of the parameter, which we can use to reach conclusions about it. The following formula shows Bayes' theorem:

All Bayesian statistics are an exercise in applying this theorem. The α symbol means proportional to, that is, that the two sides differ by a multiplicative factor.