A review of stochastic sampling methods for Bayesian inference problems

Adolphus Lye; Alice Cicirello; Edoardo Patelli

doi:10.3850/978-981-11-2724-3-1087-cd

A review of stochastic sampling methods for Bayesian inference problems

Adolphus Lye, Alice Cicirello, Edoardo Patelli

Civil And Environmental Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

9 Citations (Scopus)

89 Downloads (Pure)

Abstract

This study was done with the aim to analyze and evaluate the strengths and limitations of the Markov Chain Monte-Carlo (MCMC), Transitional Markov Chain Monte-Carlo (TMCMC), and Sequential Monte-Carlo (SMC) sampling methods in the context of solving engineering design problems. For each of these methods discussed in this paper, a case example will also be presented in the form of simple toy-model problems to demonstrate its use and effectiveness in estimating parameters under uncertainty and comparing it with determined results. For the MCMC case example, a simple harmonic oscillator will be looked into to estimate the value of the spring constant, k. For the TMCMC case example, the problem will be extended into a coupled oscillator problem and the goal would be to estimate the values of two spring constants to which there is imprecise knowledge: κ and κ12. Finally, for the SMC case example, a simple harmonic oscillator will be analyzed once again as a static linear system to estimate the spring constant, k. As such, this conference paper is also targeted at readers who are new to these methods and to provide succinct information in facilitating the understanding of the three sampling approaches.

Original language	English
Title of host publication	Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019
Editors	Michael Beer, Enrico Zio
Pages	1866-1873
Number of pages	8
ISBN (Electronic)	9789811127243
DOIs	https://doi.org/10.3850/978-981-11-2724-3-1087-cd
Publication status	Published - 26 Sept 2019
Event	29th European Safety and Reliability Conference, ESREL 2019 - Hannover, Germany Duration: 22 Sept 2019 → 26 Sept 2019

Publication series

Name	Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019

Conference

Conference	29th European Safety and Reliability Conference, ESREL 2019
Country/Territory	Germany
City	Hannover
Period	22/09/19 → 26/09/19

Funding

This research would not have been possible without the guidance and inputs from my supervisors Dr Edoardo Patelli and Dr Alice Cicirello who are also co-authors of this paper. In addition, we would also like to thank Dr Matteo Broggi from Leibniz Universität Hannover and Dr Peter Green from University of Liverpool who provided their insights on the topics shared in this paper, without which, the writing of this paper would not have been made possible as well. Finally, we would also like to thank the Institute for Risk and Uncertainty for the facilities which allowed for this research to be carried out smoothly as well as the Singapore Nuclear Research and Safety Initiatives for the sponsorship for my PhD study.

Keywords

bayesian inference
estimation methods
markov chain monte-carlo
random sampling
sequential monte-carlo
transitional markov chain monte-carlo
inference engine
safety engineering
uncertainty analysis
coupled oscillators
harmonic oscillators

Access to Document

10.3850/978-981-11-2724-3-1087-cd

Lye-etal-ESREL2019-A-review-stochastic-sampling-methods-bayesian-inference-problemsAccepted author manuscript, 678 KB

Cite this

Lye, A., Cicirello, A., & Patelli, E. (2019). A review of stochastic sampling methods for Bayesian inference problems. In M. Beer, & E. Zio (Eds.), Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019 (pp. 1866-1873). (Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019). https://doi.org/10.3850/978-981-11-2724-3-1087-cd

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title = "A review of stochastic sampling methods for Bayesian inference problems",

abstract = "This study was done with the aim to analyze and evaluate the strengths and limitations of the Markov Chain Monte-Carlo (MCMC), Transitional Markov Chain Monte-Carlo (TMCMC), and Sequential Monte-Carlo (SMC) sampling methods in the context of solving engineering design problems. For each of these methods discussed in this paper, a case example will also be presented in the form of simple toy-model problems to demonstrate its use and effectiveness in estimating parameters under uncertainty and comparing it with determined results. For the MCMC case example, a simple harmonic oscillator will be looked into to estimate the value of the spring constant, k. For the TMCMC case example, the problem will be extended into a coupled oscillator problem and the goal would be to estimate the values of two spring constants to which there is imprecise knowledge: κ and κ12. Finally, for the SMC case example, a simple harmonic oscillator will be analyzed once again as a static linear system to estimate the spring constant, k. As such, this conference paper is also targeted at readers who are new to these methods and to provide succinct information in facilitating the understanding of the three sampling approaches.",

keywords = "bayesian inference, estimation methods, markov chain monte-carlo, random sampling, sequential monte-carlo, transitional markov chain monte-carlo, inference engine, safety engineering, uncertainty analysis, coupled oscillators, harmonic oscillators",

author = "Adolphus Lye and Alice Cicirello and Edoardo Patelli",

note = "Funding Information: This research would not have been possible without the guidance and inputs from my supervisors Dr Edoardo Patelli and Dr Alice Cicirello who are also co-authors of this paper. In addition, we would also like to thank Dr Matteo Broggi from Leibniz Universit{\"a}t Hannover and Dr Peter Green from University of Liverpool who provided their insights on the topics shared in this paper, without which, the writing of this paper would not have been made possible as well. Finally, we would also like to thank the Institute for Risk and Uncertainty for the facilities which allowed for this research to be carried out smoothly as well as the Singapore Nuclear Research and Safety Initiatives for the sponsorship for my PhD study. Publisher Copyright: Copyright {\textcopyright} 2019 European Safety and Reliability Association.; 29th European Safety and Reliability Conference, ESREL 2019 ; Conference date: 22-09-2019 Through 26-09-2019",

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Lye, A, Cicirello, A & Patelli, E 2019, A review of stochastic sampling methods for Bayesian inference problems. in M Beer & E Zio (eds), Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019. Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019, pp. 1866-1873, 29th European Safety and Reliability Conference, ESREL 2019, Hannover, Germany, 22/09/19. https://doi.org/10.3850/978-981-11-2724-3-1087-cd

A review of stochastic sampling methods for Bayesian inference problems. / Lye, Adolphus; Cicirello, Alice; Patelli, Edoardo.
Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019. ed. / Michael Beer; Enrico Zio. 2019. p. 1866-1873 (Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

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N1 - Funding Information: This research would not have been possible without the guidance and inputs from my supervisors Dr Edoardo Patelli and Dr Alice Cicirello who are also co-authors of this paper. In addition, we would also like to thank Dr Matteo Broggi from Leibniz Universität Hannover and Dr Peter Green from University of Liverpool who provided their insights on the topics shared in this paper, without which, the writing of this paper would not have been made possible as well. Finally, we would also like to thank the Institute for Risk and Uncertainty for the facilities which allowed for this research to be carried out smoothly as well as the Singapore Nuclear Research and Safety Initiatives for the sponsorship for my PhD study. Publisher Copyright: Copyright © 2019 European Safety and Reliability Association.

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N2 - This study was done with the aim to analyze and evaluate the strengths and limitations of the Markov Chain Monte-Carlo (MCMC), Transitional Markov Chain Monte-Carlo (TMCMC), and Sequential Monte-Carlo (SMC) sampling methods in the context of solving engineering design problems. For each of these methods discussed in this paper, a case example will also be presented in the form of simple toy-model problems to demonstrate its use and effectiveness in estimating parameters under uncertainty and comparing it with determined results. For the MCMC case example, a simple harmonic oscillator will be looked into to estimate the value of the spring constant, k. For the TMCMC case example, the problem will be extended into a coupled oscillator problem and the goal would be to estimate the values of two spring constants to which there is imprecise knowledge: κ and κ12. Finally, for the SMC case example, a simple harmonic oscillator will be analyzed once again as a static linear system to estimate the spring constant, k. As such, this conference paper is also targeted at readers who are new to these methods and to provide succinct information in facilitating the understanding of the three sampling approaches.

AB - This study was done with the aim to analyze and evaluate the strengths and limitations of the Markov Chain Monte-Carlo (MCMC), Transitional Markov Chain Monte-Carlo (TMCMC), and Sequential Monte-Carlo (SMC) sampling methods in the context of solving engineering design problems. For each of these methods discussed in this paper, a case example will also be presented in the form of simple toy-model problems to demonstrate its use and effectiveness in estimating parameters under uncertainty and comparing it with determined results. For the MCMC case example, a simple harmonic oscillator will be looked into to estimate the value of the spring constant, k. For the TMCMC case example, the problem will be extended into a coupled oscillator problem and the goal would be to estimate the values of two spring constants to which there is imprecise knowledge: κ and κ12. Finally, for the SMC case example, a simple harmonic oscillator will be analyzed once again as a static linear system to estimate the spring constant, k. As such, this conference paper is also targeted at readers who are new to these methods and to provide succinct information in facilitating the understanding of the three sampling approaches.

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KW - estimation methods

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KW - random sampling

KW - sequential monte-carlo

KW - transitional markov chain monte-carlo

KW - inference engine

KW - safety engineering

KW - uncertainty analysis

KW - coupled oscillators

KW - harmonic oscillators

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A review of stochastic sampling methods for Bayesian inference problems

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