Gibbs sampling, exponential families and orthogonal polynomials

By Persi Diaconis, Kshitij Khare, L. Saloff‐Coste. 2008

152 citations recorded by the source corpus.

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.

Subfields: Analytical Chemistry, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c2d948119805767565dd1caaec31c14f77a7f746

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In Analytical Chemistry

In Statistics and Probability

Citations in the corpus

An introduction to multivariate Krawtchouk polynomials and their applications (2013, background): “This property was discovered and exploited by Eagleson (1969) in his solution of the Lancaster problem for the Binomial distribution. Vere-Jones (1971) and Dunkl and Ramirez (1974) study group theoretic properties of the hypergroup property of the Krawtchouk polynomials.”
RATES OF CONVERGENCE OF SOME MULTIVARIATE MARKOV CHAINS WITH POLYNOMIAL EIGENFUNCTIONS (2009, methodology): “One of their motivating examples is how fast the classical beta-binomial Gibbs sampler converges ([11], Proposition 1).”
A spectral analytic comparison of trace-class data augmentation algorithms and their sandwich variants (2011, background): “But {gi}∞i=1 form an orthonormal basis of L20(fX), which proves that K has eigenvalues {β2i }∞i=1.”
The Markov chain Monte Carlo revolution (2008, methodology): “Here is an example with an infinite state space drawn from my work with Khare and Saloff-Coste [23] where this program can be usefully pushed through.”