Optimal scaling of Metropolis algorithms: Heading toward general target distributions |
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| Authors: | Mylène Bédard Jeffrey S Rosenthal |
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| Institution: | 1. Département de mathématiques et de statistique Université de Montréal, C. P. 6128, succursale Centre‐ville Montréal (Québec) Canada H3C 3J7;2. This article is based in part on Myléne Bédard's doctoral dissertation, which was selected as the winner of the 2006 Pierre Robillard Award of the Statistical Society of Canada. The thesis supervisor was Jeffrey S. Rosenthal. /Cet article est basé en partie sur la thése de Myléne Bédard, récipiendaire du prix Pierre‐Robillard de la Société statistique du Canada pour l'année 2006. La direction de thése a été assumée par Jeffrey S. Rosenthal.;3. Department of Statistics, University of Toronto 100 St. George Street, Toronto, Ontario Canada M5S 3G3 |
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| Abstract: | The authors provide an overview of optimal scaling results for the Metropolis algorithm with Gaussian proposal distribution. They address in more depth the case of high‐dimensional target distributions formed of independent, but not identically distributed components. They attempt to give an intuitive explanation as to why the well‐known optimal acceptance rate of 0.234 is not always suitable. They show how to find the asymptotically optimal acceptance rate when needed, and they explain why it is sometimes necessary to turn to inhomogeneous proposal distributions. Their results are illustrated with a simple example. |
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| Keywords: | Acceptance rate Langevin diffusion marginal process Metropolis algorithm Scaling weak convergence |
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