Gibbs Sampling, Exponential Families and Orthogonal Polynomials
نویسندگان
چکیده
منابع مشابه
Gibbs Sampling, Exponential Families and Orthogonal Polynomials
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.
متن کاملComment: Gibbs Sampling, Exponential Families and Orthogonal Polynomials
Patrizia Berti is Professor, Dipartimento di Matematica Pura ed Applicata “G. Vitali”, Universita’ di Modena e Reggio-Emilia, via Campi 213/B, 41100 Modena, Italy e-mail: [email protected]. Guido Consonni is Professor, Dipartimento di Economia Politica e Metodi Quantitativi, Universita’ di Pavia, via S. Felice 5, 27100 Pavia, Italy e-mail: [email protected]. Luca Pratelli is Profe...
متن کاملComment: Gibbs Sampling, Exponential Families, and Orthogonal Polynomials
It is our pleasure to congratulate the authors (hereafter DKSC) on an interesting paper that was a delight to read. While DKSC provide a remarkable collection of connections between different representations of the Markov chains in their paper, we will focus on the “running time analysis” portion. This is a familiar problem to statisticians; given a target population, how can we obtain a repres...
متن کاملRejoinder: Gibbs Sampling, Exponential Families and Orthogonal Polynomials
We are thankful to the discussants for their hard, interesting work. The main purpose of our paper was to give reasonably sharp rates of convergence for some simple examples of the Gibbs sampler. We chose examples from expository accounts where direct use of available techniques gave practically useless answers. Careful treatment of these simple examples grew into bivariate modeling and Lancast...
متن کاملDiscussion of “Gibbs sampling, exponential families, and orthogonal polynomials” by Diaconis, Khare, and Saloff-Coste
It is our pleasure to congratulate the authors (hereafter DKSC) on an interesting paper that was a delight to read. While DKSC provide a remarkable collection of connections between different representations of the Markov chains in their paper, we will focus on the “running time analysis” portion. This is a familiar problem to statisticians; given a target population, how can we obtain a repres...
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ژورنال
عنوان ژورنال: Statistical Science
سال: 2008
ISSN: 0883-4237
DOI: 10.1214/07-sts252