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February 1996 Convergence properties of the Gibbs sampler for perturbations of Gaussians
Yali Amit
Ann. Statist. 24(1): 122-140 (February 1996). DOI: 10.1214/aos/1033066202


The exact second eigenvalue of the Markov operator of the Gibbs sampler with random sweep strategy for Gaussian densities is calculated. A comparison lemma yields an upper bound on the second eigenvalue for bounded perturbations of Gaussians which is a significant improvement over previous bounds. For two-block Gibbs sampler algorithms with a perturbation of the form $\chi(g_1(x^{(1)}) + g_2(x^{(2)}))$ the derivative of the second eigenvalue of the algorithm is calculated exactly at $\chi = 0$, in terms of expectations of the Hessian matrices of $g_1$ and $g_2$.


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Yali Amit. "Convergence properties of the Gibbs sampler for perturbations of Gaussians." Ann. Statist. 24 (1) 122 - 140, February 1996.


Published: February 1996
First available in Project Euclid: 26 September 2002

zbMATH: 0854.60066
MathSciNet: MR1389883
Digital Object Identifier: 10.1214/aos/1033066202

Primary: 47B38 , 60J10

Keywords: Integral‎ ‎Operators , Markov chains , second Eigenvalue

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 1 • February 1996
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