Bayesian estimation and inference

Abstract Bayesian methods allow researchers to combine precise descriptions of prior beliefs with new data in a principled way. The main object of interest in Bayesian statistics is the posterior distribution, which describes the uncertainty associated with parameters given prior beliefs about them and the observed data. The posterior can be difficult to compute mathematically, but computational methods can give arbitrarily good approximations in most cases. Bayesian point and interval estimates are features of the posterior, such as measures of its central tendency or intervals into which the parameter falls with specified probability. Bayesian hypothesis testing is complicated and controversial, but one relevant tool is the Bayes factor, which compares the probability of observing the data under a pair of distinct hypotheses.