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Monte Carlo sampling methods using Markov chains and their applications

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  • W. K. Hastings

Abstract

SummaryA generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.

Suggested Citation

  • W. K. Hastings, 1970. "Monte Carlo sampling methods using Markov chains and their applications," Biometrika, Biometrika Trust, vol. 57(1), pages 97-109.
    • Handle: RePEc:oup:biomet:v:57:y:1970:i:1:p:97-109.
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    File URL: http://hdl.handle.net/10.1093/biomet/57.1.97
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    Cited by:

    1. Tabandeh, Armin & Jia, Gaofeng & Gardoni, Paolo, 2026. "Langevin importance sampling for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 266(PA).
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    4. Mahendra Saha & Govindasamy Gopal & Abhimanyu Singh Yadav, 2025. "Bayesian estimation of the process capability index $${\mathcal {C}}_{pc}$$ C pc under type II progressive censoring scheme," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 16(12), pages 4069-4085, December.
    5. Amal S. Hassan & Ehab M. Almetwally, 2026. "Statistical Inference for Multi-Stress-Strength Reliability Under Inverse Weibull Distribution with Progressive Type II Censoring and Random Removal," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 88(1), pages 252-291, February.
    6. Shuchismita Sarkar & Volodymyr Melnykov, 2025. "Detecting Anomalies in European Trade Data Using Directed Weighted Multilayer Dynamic Networks," Journal of Classification, Springer;The Classification Society, vol. 42(3), pages 544-564, November.
    7. Kevin Duijndam & Ger Koole & Rob Mei, 2025. "Bayesian reinforcement learning to optimize paid ancillary revenue in the airline industry," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 24(6), pages 551-567, December.
    8. Franco Bagnoli & Tommaso Matteuzzi, 2025. "Metastability in the diluted parallel Ising model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 98(10), pages 1-10, October.
    9. Mitra Kharabati & Morteza Amini & Mohammad Arashi, 2026. "Variational inference for sparse poisson regression," Computational Statistics, Springer, vol. 41(3), pages 1-50, April.
    10. Mylène Bédard, 2025. "Non-stationary Phase of the Metropolis-adjusted Langevin Algorithm with Annealed Proposals," Methodology and Computing in Applied Probability, Springer, vol. 27(4), pages 1-40, December.
    11. Andrés Ramírez–Hassan & Juan David Rengifo–Castro & Miguel Manzur & Estephania Rueda-Ramírez, 2025. "Approximate Bayesian computation to estimate persistent and transient efficiency in stochastic frontier panel data models," Journal of Productivity Analysis, Springer, vol. 64(2), pages 145-166, October.
    12. Matthias Schmal & Patrick Mäder, 2026. "Reliable uncertainty estimates in deep learning with efficient Metropolis-Hastings algorithms," Nature Communications, Nature, vol. 17(1), pages 1-12, December.
    13. Xiao, Sinan & Nowak, Wolfgang, 2026. "Reliability sensitivity analysis with multiple failure domains based on an extended two-stage Markov chain Monte Carlo simulation," Reliability Engineering and System Safety, Elsevier, vol. 266(PA).

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