Gibbs Sampling, Exponential Families and Orthogonal Polynomials
Persi Diaconis, Kshitij Khare, and Laurent Saloff-Coste
Source: Statist. Sci. Volume 23, Number 2 (2008), 151-178.
Abstract
We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their conjugate priors. In each case, the transition operator is explicitly diagonalizable with classical orthogonal polynomials as eigenfunctions.
Keywords: Gibbs sampler; running time analyses; exponential families; conjugate priors; location families; orthogonal polynomials; singular value decomposition
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