Bayesian Inference and Markov Chain Monte Carlo
Faming Liang, Chuanhai Liu, Raymond James Carroll · 2010
By its nature, Bayesian inference is necessarily subjective because specification of the full Bayesian model amounts to practically summarizing available information in terms of precise probabilities. The concept of Bayes factors is introduced in the situation with a common observed data and two competing hypotheses. This chapter provides a brief review of the methods that are often used for sampling from distributions for which the inverse-cdf method does not work, including the transformation methods, acceptance rejection methods, ratio-of-uniform methods, adaptive direction sampling, and perfect sampling. The total variation distance between two measures is used to describe the convergence of a Markov chain in the following theorem. Controlled Vocabulary Terms Bayesian Inference; random variables