Convergence and accuracy of Gibbs sampling for conditional distributions in generalized linear models
The Annals of Statistics · 1999 · Volume 27 · Issue 1
Abstract
This paper presents convergence conditions for a Markov chain constructed using Gibbs sampling, when the equilibrium distribution is the conditional sampling distribution of sufficient statistics from a generalized linear model. For cases when this unidimensional sampling is done approximately rather than exactly, the difference between the target equilibrium distribution and the resulting equilibrium distribution is expressed in terms of the difference between the true and approximating univariate conditional distributions. These methods are applied to an algorithm facilitating approximate conditional inference in canonical exponential families.
Keywords
60J20, 62E20, Markov chain Monte Carlo, saddlepoint approximations
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