Metropolis methods, gaussian proposals and antithetic variables

PJ Green; XL Han

doi:10.1007/978-1-4612-2920-9_10

Metropolis methods, gaussian proposals and antithetic variables

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Abstract

We investigate various aspects of a class of dynamic Monte Carlo methods, that generalises the Metropolis algorithm and includes the Gibbs sampler as a special case. These can be used to estimate expectations of marginal distributions in stochastic systems. A distinction is drawn between speed of weak convergence and precision of estimation. For continuously distributed processes, a particular gaussian proposal distribution is suggested: this incorporates a parameter that may be varied to improve the performance of the sampling method, by adjusting the magnitude of an “antithetic” element introduced into the sampling. The suggestion is examined in detail in some experiments based on an image analysis problem.

Translated title of the contribution	Metropolis methods, gaussian proposals and antithetic variables
Original language	English
Title of host publication	Stochastic Models, Statistical Methods, and Algorithms in Image Analysis
Editors	P Barone, A Frigessi, M Piccioni
Publisher	Springer, New York, NY
Pages	44-66
Number of pages	23
DOIs	https://doi.org/10.1007/978-1-4612-2920-9_10
Publication status	Published - 1991

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title = "Metropolis methods, gaussian proposals and antithetic variables",

abstract = "We investigate various aspects of a class of dynamic Monte Carlo methods, that generalises the Metropolis algorithm and includes the Gibbs sampler as a special case. These can be used to estimate expectations of marginal distributions in stochastic systems. A distinction is drawn between speed of weak convergence and precision of estimation. For continuously distributed processes, a particular gaussian proposal distribution is suggested: this incorporates a parameter that may be varied to improve the performance of the sampling method, by adjusting the magnitude of an “antithetic” element introduced into the sampling. The suggestion is examined in detail in some experiments based on an image analysis problem.",

author = "PJ Green and XL Han",

year = "1991",

doi = "10.1007/978-1-4612-2920-9_10",

language = "English",

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editor = "P Barone and A Frigessi and M Piccioni",

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AU - Han, XL

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N2 - We investigate various aspects of a class of dynamic Monte Carlo methods, that generalises the Metropolis algorithm and includes the Gibbs sampler as a special case. These can be used to estimate expectations of marginal distributions in stochastic systems. A distinction is drawn between speed of weak convergence and precision of estimation. For continuously distributed processes, a particular gaussian proposal distribution is suggested: this incorporates a parameter that may be varied to improve the performance of the sampling method, by adjusting the magnitude of an “antithetic” element introduced into the sampling. The suggestion is examined in detail in some experiments based on an image analysis problem.

AB - We investigate various aspects of a class of dynamic Monte Carlo methods, that generalises the Metropolis algorithm and includes the Gibbs sampler as a special case. These can be used to estimate expectations of marginal distributions in stochastic systems. A distinction is drawn between speed of weak convergence and precision of estimation. For continuously distributed processes, a particular gaussian proposal distribution is suggested: this incorporates a parameter that may be varied to improve the performance of the sampling method, by adjusting the magnitude of an “antithetic” element introduced into the sampling. The suggestion is examined in detail in some experiments based on an image analysis problem.

U2 - 10.1007/978-1-4612-2920-9_10

DO - 10.1007/978-1-4612-2920-9_10

M3 - Chapter in a book

SP - 44

EP - 66

BT - Stochastic Models, Statistical Methods, and Algorithms in Image Analysis

A2 - Barone, P

A2 - Frigessi, A

A2 - Piccioni, M

PB - Springer, New York, NY

ER -

Metropolis methods, gaussian proposals and antithetic variables

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