Gibbs Sampling, Exponential Families and Orthogonal Polynomials

Details Gibbs Sampling, Exponential Families and Orthogonal Polynomials Gibbs Sampling, Exponential Families and Orthogonal Polynomials

2008-08-28

arxiv.org/abs/0808.3852v1

Statistical Science 2008, Vol. 23, No. 2, 151-178

Statistics

Methodology

This paper commented in: [arXiv:0808.3855], [arXiv:0808.3856], [arXiv:0808.3859], [arXiv:0808.3861]. Rejoinder in [arXiv:0808.

Scientific paper

10.1214/07-STS252

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.

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