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Abstract: This paper analyzes the Gibbs sampler applied to a standard variance component model, and considers the question of how many iterations are required for convergence. It is proved that for K location parameters, with J observations each, the number of iterations required for convergence (for large K and J) is a constant times 1 + . This is one of the first rigorous, a priori results about time to convergence for the Gibbs sampler. A quantitative version of the theory of Harris recurrence ... (Update)
Context of citations to this paper: More
.... chains, the notion of Harris recurrence (see [A] AN] N] has proven useful in obtaining rates of convergence (see e.g. T] R2] [R3]) Finite state space Markov chains remain the simplest case to study, because their convergence can be analyzed directly in terms of...
.... and stochastic algorithms ( How long do you have to run the algorithm until the answers are satisfactory ; see e.g. GS] and [R]) In each case, it is desired to know how long a Markov chain should be run until it has converged to the desired stationary distribution....
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BibTeX entry: (Update)
Rosenthal, J. (1991), "Rates of Convergence for Gibbs Sampling for Variance Component Models," Technical Report, Harvard University, Dept. of Mathematics. http://citeseer.ist.psu.edu/article/rosenthal91rates.html More
@misc{ rosenthal91rates,
author = "J. Rosenthal",
title = "Rates of Convergence for Gibbs Sampling for Variance Component Models",
text = "Rosenthal, J. (1991), Rates of Convergence for Gibbs Sampling for Variance
Component Models, Technical Report, Harvard University, Dept. of Mathematics.",
year = "1991",
url = "citeseer.ist.psu.edu/article/rosenthal91rates.html" }
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135 Inference from iterative simulation using multiple sequences (context) - Gelman, Rubin - 1993
106 Group Representations in Probability and Statistics (context) - Diaconis - 1988
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40 A new approach to the limit theory of recurrent Markov chain.. (context) - Athreya, Ney - 1978
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