Markov chain Monte Carlo methods in Bayesian inference.

Venkatesan, P.

Applied Bayesian Statistical Analysis. Proceedings of NSABSA; 2008; 9-18.

Abstract: The Markov Chain Monte-Carlo (MCMC) born in early 1950s has recently aroused great interest among statisticians, particularly researchers in image analysis, discrete optimization, neural networks, genetic sequencing and other related fields. Recent theoretical achievements in resampling procedures provide a new perspective for handling errors in Bayesian inference, which treats all unknowns as random variables. The unknowns include uncertainties in the model such as fixed effects, random effects, unobserved indicator variables and missing data. Only in few cases, the posterior distribution is in standard analytic form. In most other models like generalized linear models, mixture models, epidemiological models and survival analysis, the exact analytic Bayesian inference is impossible. This paper surveys some of the recent advances in this area that allows exact Bayesian computation using simulations and discusses some applications to biomedical data.

Keywords : Bayesian inference, Markov Chain Monte Carlo, Gibbs, Metropolis, mixture model, hierarchical model, ECM algorithm, panic attack

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