Convergence properties of the Gibbs sampler for perturbations of Gaussians
The Annals of Statistics · 1996 · Volume 24 · Issue 1
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 $g_2$.
Keywords
47B38; 60J10; Integral Operators; Markov chains; second Eigenvalue;
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