TY - GEN
T1 - A review of stochastic sampling methods for Bayesian inference problems
AU - Lye, Adolphus
AU - Cicirello, Alice
AU - Patelli, Edoardo
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.
PY - 2019/9/26
Y1 - 2019/9/26
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.
KW - bayesian inference
KW - estimation methods
KW - markov chain monte-carlo
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
UR - http://www.scopus.com/inward/record.url?scp=85089198755&partnerID=8YFLogxK
U2 - 10.3850/978-981-11-2724-3-1087-cd
DO - 10.3850/978-981-11-2724-3-1087-cd
M3 - Conference contribution book
AN - SCOPUS:85089198755
T3 - Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019
SP - 1866
EP - 1873
BT - Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019
A2 - Beer, Michael
A2 - Zio, Enrico
T2 - 29th European Safety and Reliability Conference, ESREL 2019
Y2 - 22 September 2019 through 26 September 2019
ER -