The Annals of Statistics

Convergence properties of the Gibbs sampler for perturbations of Gaussians

Yali Amit

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Abstract

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 $g_2$.

Article information

Source
Ann. Statist. Volume 24, Number 1 (1996), 122-140.

Dates
First available in Project Euclid: 26 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1033066202

Digital Object Identifier
doi:10.1214/aos/1033066202

Mathematical Reviews number (MathSciNet)
MR1389883

Zentralblatt MATH identifier
0854.60066

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 47B38: Operators on function spaces (general)

Keywords
Second eigenvalue Markov chains integral operators

Citation

Amit, Yali. Convergence properties of the Gibbs sampler for perturbations of Gaussians. Ann. Statist. 24 (1996), no. 1, 122--140. doi:10.1214/aos/1033066202. https://projecteuclid.org/euclid.aos/1033066202


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