Gibbs Sampling, Exponential Families and Orthogonal Polynomials
Methodology
2008-10-01 v1 Classical Analysis and ODEs
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.
Cite
@article{arxiv.0808.3852,
title = {Gibbs Sampling, Exponential Families and Orthogonal Polynomials},
author = {Persi Diaconis and Kshitij Khare and Laurent Saloff-Coste},
journal= {arXiv preprint arXiv:0808.3852},
year = {2008}
}
Comments
This paper commented in: [arXiv:0808.3855], [arXiv:0808.3856], [arXiv:0808.3859], [arXiv:0808.3861]. Rejoinder in [arXiv:0808.3864]. Published in at http://dx.doi.org/10.1214/07-STS252 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)