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Optimum Monte-Carlo sampling using Markov chains
Abstract
The sampling method proposed by Metropolis et al. (1953) requires the simulation of a Markov chain with a specified π as its stationary distribution. Hastings (1970) outlined a general procedure for constructing and simulating such a Markov chain. The matrix P of transition probabilities is constructed using a defined symmetric function sij and an arbitrary transition matrix Q. Here, for a given Q, the relative merits of the two simple choices for sij suggested by Hastings (1970) are discussed. The optimum choice for sij is shown to be one of these. For the other choice, those Q are given which are known to make the sampling method based on P asymptotically less precise than independent sampling.
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Cites
Equation of State Calculations by Fast Computing Machines
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953) · The Journal of Chemical Physics · doi:10.1063/1.1699114 · Cited by 37,192
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Computer Simulation of Liquids
Allen, M. P., & Tildesley, D. J. (2017) · doi:10.1093/oso/9780198803195.001.0001 · Cited by 20,945
An introduction to MCMC for machine learning.
Andrieu, C., de Freitas, N., Doucet, A., & Jordan, M. I. (2003) · Machine Learning · doi:10.1023/a:1020281327116 · Cited by 2,451
Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods
Smith, A. F. M., & Roberts, G. O. (1993) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1993.tb01466.x · Cited by 1,713
(1997) · Cited by 1,193
Markov chain Monte Carlo method and its application
Brooks, S. (1998) · Journal of the Royal Statistical Society: Series D (The Statistician) · doi:10.1111/1467-9884.00117 · Cited by 843
Metadata
- Authors
- PESKUN, P. H.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1973
- Volume
- 60
- Issue
- 3
- Pages
- 607-612
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2122891730
- Cited by
- 531
- References
- 1
- FWCI
- 0.61
- Type
- journal article
- Language
- en
- Open access
- closed
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