Basic Ideas of Bayesian Methods

Abstract

This chapter is devoted to some basic ideas on the Bayesian approach to statistical inference, where the parameter is treated as a random variable, which is assigned a distribution. This distribution – the prior distribution – represents the prior knowledge about the parameter before observing the data. Once the data is observed, the inference about parameter is drawn from the posterior distribution – the conditional distribution of parameter given the data. The term “Bayesian” comes from the well-known Bayes theorem, which is a formula for computing the posterior probabilities.