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Optimal scaling of Metropolis algorithms: Heading toward general target distributions
Author(s) -
Bédard Mylène,
Rosenthal Jeffrey S.
Publication year - 2008
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.5550360401
Subject(s) - heading (navigation) , simple (philosophy) , scaling , independent and identically distributed random variables , gaussian , algorithm , distribution (mathematics) , asymptotically optimal algorithm , computer science , mathematics , mathematical optimization , statistical physics , random variable , statistics , mathematical analysis , geometry , physics , philosophy , geodesy , epistemology , quantum mechanics , geography
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.