Easy-to-Apply Results for Establishing Convergence of Markov Chains in Bayesian Analysis

TL;DRAbstract

Abstract : The Markov chain simulation method has become a powerful computational method in Bayesian analysis. The success of this method depends on the convergence of the Markov chain to its stationary distribution. We give two carefully stated theorems, whose conditions are easy to verify, that establish this convergence. We give versions of our conditions which are simpler to verify for the Markov chains that arise most commonly in Bayesian analysis.... Bayesian Poisson regression; Calculation of posterior distributions; Ergodic theorem; Markov chain simulation method.

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