Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo
Journal of the American Statistical AssociationPublished 1 June 1995
Jeffrey S. Rosenthal
Citations463
SJR quartileQ1
SJR score4.10
SNIP3.08
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Abstract
Abstract General methods are provided for analyzing the convergence of discrete-time, general state-space Markov chains, such as those used in stochastic simulation algorithms including the Gibbs sampler. The methods provide rigorous, a priori bounds on how long these simulations should be run to give satisfactory results. Results are applied to two models of the Gibbs sampler: a bivariate normal model, and a hierarchical Poisson model (with gamma conditionals). The methods use the notion of minorization conditions for Markov chains. Key Words: Bivariate normal modelCouplingDrift conditionGibbs samplerHarris recurrenceHierarchical Poisson modelMetropolis-Hastings algorithmRegeneration time
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