The Annals of Statistics

Convergence properties of the Gibbs sampler for perturbations of Gaussians

Yali Amit

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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

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

First available in Project Euclid: 26 September 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Second eigenvalue Markov chains integral operators


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.

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