Bayesian Regression and Classification

Abstract

1 Introduction Although Bayesian methods have been studied for many years, it is only recently that theirpractical application has become truly widespread. This is due in large part to the relatively high computational overhead of performing the marginalizations (integrations and summa-tions) which lie at the heart of the Bayesian paradigm. For this reason more traditional approaches, based on point estimation of parameters, have typically been the method of choice.However, the widespread availability of fast computers allows Bayesian computations to be performed in reasonable time for an increasingly wide spectrum of real world applications.Furthermore, the development of Markov chain Monte Carlo techniques, and more recently of deterministic approximation schemes such as variational inference, have greatly extendedthe range of models amenable to a Bayesian treatment.