article

A guided walk Metropolis algorithm

Author:

Paul GustafsonAuthors Info & Claims

Statistics and Computing, Volume 8, Issue 4

Pages 357 - 364

https://doi.org/10.1023/A:1008880707168

Published: 01 December 1998 Publication History

Abstract

The random walk Metropolis algorithm is a simple Markov chain Monte Carlo scheme which is frequently used in Bayesian statistical problems. We propose a guided walk Metropolis algorithm which suppresses some of the random walk behavior in the Markov chain. This alternative algorithm is no harder to implement than the random walk Metropolis algorithm, but empirical studies show that it performs better in terms of efficiency and convergence time.

References

[1]

Besag, J., Green, P., Higdon, D. and Mengersen, K. (1995) Bayesian computation and stochastic systems (with discussion). Statistical Science, 10, 3-36.

[2]

Diaconis, P., Holmes, S. and Neal, R. M. (1997) Analysis of a non-reversible Markov chain sampler. Technical Report BU- 1385-M, Biometrics Unit, Cornell University.

[3]

Duane, S., Kennedy, A. D., Pendleton, B. J. and Roweth, D. (1987) Hybrid Monte Carlo. Physics Letters B, 195, 216- 222.

[4]

Gelfand, A. E. and Smith, A. F. M. (1990) Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398-409.

[5]

Gelman, A., Roberts, G. and Gilks W. (1996) Efficient Metropolis jumping rules, in Bayesian Statistics 5, Berger, J. O., Bernardo, J. M., Dawid, A. P. and Smith, A. F. M. (eds), Oxford University Press.

[6]

Geman, S. and Geman, D. (1984) Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.

[7]

Greenhouse, J. and Wasserman, L. (1996) A practical robust method for Bayesian model selection: a case study in the analysis of clinical trials, in Bayesian Robustness Berger, J. O., Betro, B., Moreno, E., Pericchi, L. R., Ruggeri, F., Salinetti, G. and Wasserman, L. (eds), Institute of Mathematical Statistics Lecture Notes - Monograph Series, pp. 41-58.

[8]

Hastings, W. K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97- 109.

[9]

Horowitz, A. M. (1991) A generalized guided Monte Carlo algorithm. Physics Letters B, 268, 247-252.

[10]

Kass, R. E., Carlin, B. P., Gelman, A. and Neal, R. M. (1998) Markov chain Monte Carlo in practice: a roundtable discussion. The American Statistician, 52, 93-100.

[11]

Kuo, L. and Yang, T. Y. (1996) Bayesian computation for nonhomogeneous Poisson processes in software reliability. Journal of the American Statistical Association, 91, 763-773.

[12]

Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953) Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087-1092.

[13]

Muller, P. and Rios Insua, D. (1995) Issues in Bayesian analysis of neural network models. Working Paper 95-31, Institute of Statistics and Decision Sciences, Duke University.

[14]

Muller, P. and Roeder, K. (1997) A Bayesian semiparametric model for case-control studies with errors in variables. Biometrika , 84, 523-537.

[15]

Neal, R. M. (1993) Probabilistic inference using Markov Chain Monte Carlo methods. Technical Report CRG-TR-93-1, Department of Computer Science, University of Toronto.

[16]

Neal, R. M. (1995) Suppressing random walks in Markov Chain Monte Carlo using ordered overrelaxation. Technical Report 9508, Department of Statistics, University of Toronto.

[17]

Newton, M. A., Czado, C. and Chappell, R. (1996) Bayesian inference for semiparametric binary regression. Journal of the American Statistical Association, 91, 142-153.

[18]

Roberts, G. O., Gelman, A. and Gilks, W. (1997) Weak convergence and optimal scaling of random walk Metropolis algorithms. Annals of Applied Probability, 7, 110-120.

[19]

Roberts, G. O. and Rosenthal, J. S. (1998) Optimal scaling of discrete approximations to Langevin diffusions. Journal of the Royal Statistical Society B, to appear.

[20]

Sargent, D. J. (1997) A flexible approach to time-varying coefficients in the Cox regression setting. Lifetime Data Analysis, 3, 13-25.

[21]

Sargent, D. J. (1998) A general framework for random effects survival analysis in the Cox proportional hazards setting. Biometrics, 54, to appear.

[22]

Smith, A. F. M. and Roberts, G. O. (1994) Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods (with discussion). Journal of the Royal Statistical Society B, 55, 3-23.

[23]

Tierney, L. (1994) Markov chains for exploring posterior distributions (with discussion). Annals of Statistics, 22, 1701-1762.

[24]

Verdinelli and Wasserman (1998) Bayesian goodness of fit testing using infinite dimensional exponential families. Annals of Statistics, 26, 1215-1241.

[25]

Waller, L. A., Carlin, B. P., Xia, H. and Gelfand, A. E. (1997) Hierarchical spatio-temporal mapping of disease rates. Journal of the American Statistical Association, 92, 607-617.

Cited By

Vialaret MMaire F(2020)On the Convergence Time of Some Non-Reversible Markov Chain Monte Carlo MethodsMethodology and Computing in Applied Probability10.1007/s11009-019-09766-w22:3(1349-1387)Online publication date: 1-Sep-2020
https://dl.acm.org/doi/10.1007/s11009-019-09766-w
Yıldırım SErmiş B(2019)Exact MCMC with differentially private movesStatistics and Computing10.1007/s11222-018-9847-x29:5(947-963)Online publication date: 1-Sep-2019
https://dl.acm.org/doi/10.1007/s11222-018-9847-x
Gustafson PMacnab YWen S(2004)On the Value of derivative evaluations and random walk suppression in Markov Chain Monte Carlo algorithmsStatistics and Computing10.1023/B:STCO.0000009413.87656.ef14:1(23-38)Online publication date: 1-Jan-2004
https://dl.acm.org/doi/10.1023/B%3ASTCO.0000009413.87656.ef

A guided walk Metropolis algorithm
1. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic reasoning algorithms

Recommendations

Bayesian Analysis of Mixture Normal Model via Equi-Energy Sampler and Improved Metropolis-Hastings Algorithm
CYBERC '15: Proceedings of the 2015 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery

Mixture normal model provides a convenient and flexible probabilistic representation of heterogeneous data, and the estimation of parameters received considerable attention in recent years. In this paper, we propose a Bayesian analysis of mixture normal ...
On the Value of derivative evaluations and random walk suppression in Markov Chain Monte Carlo algorithms

Two strategies that can potentially improve Markov Chain Monte Carlo algorithms are to use derivative evaluations of the target density, and to suppress random walk behaviour in the chain. The use of one or both of these strategies has been investigated ...
Analyzing Markov chain Monte Carlo output
Abstract
Markov chain Monte Carlo (MCMC) is a sampling‐based method for estimating features of probability distributions. MCMC methods produce a serially correlated, yet representative, sample from the desired distribution. As such it can be difficult to ...
Visual representation of the multivariate correlation structure in a Markov chain. Output analysis that accounts for this multivariate structure is able to more accurately summarize variability in the simulation process. We review the output analysis ...

Comments

Information & Contributors

Information

Published In

cover image Statistics and Computing

Statistics and Computing Volume 8, Issue 4

December 1998

111 pages

ISSN:0960-3174

Issue’s Table of Contents

Copyright © Copyright © 1998 Kluwer Academic Publishers.

Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 01 December 1998

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

3
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 12 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

Vialaret MMaire F(2020)On the Convergence Time of Some Non-Reversible Markov Chain Monte Carlo MethodsMethodology and Computing in Applied Probability10.1007/s11009-019-09766-w22:3(1349-1387)Online publication date: 1-Sep-2020
https://dl.acm.org/doi/10.1007/s11009-019-09766-w
Yıldırım SErmiş B(2019)Exact MCMC with differentially private movesStatistics and Computing10.1007/s11222-018-9847-x29:5(947-963)Online publication date: 1-Sep-2019
https://dl.acm.org/doi/10.1007/s11222-018-9847-x
Gustafson PMacnab YWen S(2004)On the Value of derivative evaluations and random walk suppression in Markov Chain Monte Carlo algorithmsStatistics and Computing10.1023/B:STCO.0000009413.87656.ef14:1(23-38)Online publication date: 1-Jan-2004
https://dl.acm.org/doi/10.1023/B%3ASTCO.0000009413.87656.ef

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents