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Kolassa, John E.

Convergence and accuracy of Gibbs sampling for conditional distributions in generalized linear models. (English) Zbl 0932.62078

Ann. Stat. 27, No. 1, 129-142 (1999).
Summary: 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.

MSC:

62J12 Generalized linear models (logistic models)
65C40 Numerical analysis or methods applied to Markov chains
62E20 Asymptotic distribution theory in statistics

Keywords:

Markov chain Monte Carlo; saddlepoint approximations
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References:

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[23] ROCHESTER, NEW YORK 14642 E-MAIL: kolassa@bio1.bst.rochester.edu
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