A Geometric Interpretation of the Metropolis-Hastings Algorithm

Louis J. Billera, Persi Diaconis

Type: Article

Publication Date: 2001-11-01

Citations: 68

DOI: https://doi.org/10.1214/ss/1015346318

Abstract

The Metropolis–Hastings algorithm transforms a given stochastic matrix into a reversible stochastic matrix with a prescribed stationary distribution. We show that this transformation gives the minimum distance solution in an $L^1$ metric.

Locations

Statistical Science - View - PDF
CiteSeer X (The Pennsylvania State University) - View - PDF

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Works Cited by This (8)

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+ PDF Chat	Rates of convergence of the Hastings and Metropolis algorithms	1996	Kerrie Mengersen Richard L. Tweedie
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+ PDF Chat	Weak convergence and optimal scaling of random walk Metropolis algorithms	1997	Susan A. Gelman Walter R. Gilks Gareth O. Roberts
+	Optimum Monte-Carlo sampling using Markov chains	1973	Peter H. Peskun
+	Monte Carlo sampling methods using Markov chains and their applications	1970	W. Keith Hastings
+	Monte Carlo Methods	1964	J. M. Hammersley D. C. Handscomb
+ PDF Chat	Eigen-analysis for some examples of the Metropolis algorithm	1992	Persi Diaconis Phil Hanlon
+ PDF Chat	Analysis of systematic scan Metropolis algorithms using Iwahori-Hecke algebra techniques.	2000	Persi Diaconis Arun Ram