Basic Elements of Bayesian Statistics

Abstract

A review of Bayesian estimation and testing methods is given that is not a thorough overview but concentrates on some speci_c elements. First, simulation-based methods for parameter estimation, like the Gibbs sampling and the Metropolis-Hastings algorithms, from the general class of Markov chain Monte Carlo algorithms, are discussed. Second, the Bayesian approach to model selection and hypothesis testing is presented. The techniques and methods described in this chapter are needed to completely exploit the Bayesian machinery for item response modeling.