A review of stochastic sampling methods for Bayesian inference problems


Lye, A, Cicirello, A and Patelli, E ORCID: 0000-0002-5007-7247 (2020) A review of stochastic sampling methods for Bayesian inference problems. In: European Safety and Reliability Conference, 2019-9-22 - 2019-9-26, Hannover, Germany.

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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.

Item Type: Conference or Workshop Item (Unspecified)
Uncontrolled Keywords: Bayesian Inference, Random Sampling, Estimation Methods, Markov Chain Monte-Carlo, Transitional Markov Chain Monte-Carlo, Sequential Monte-Carlo
Depositing User: Symplectic Admin
Date Deposited: 04 Jun 2019 08:04
Last Modified: 19 Jan 2023 00:41
DOI: 10.3850/978-981-11-2724-3-1087-cd
URI: https://livrepository.liverpool.ac.uk/id/eprint/3043863
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