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Bayesian inference with reliability methods without knowing the maximum of the likelihood function

Betz, Wolfgang and Beck, James L. and Papaioannou, Iason and Straub, Daniel (2018) Bayesian inference with reliability methods without knowing the maximum of the likelihood function. Probabilistic Engineering Mechanics, 53 . pp. 14-22. ISSN 0266-8920. doi:10.1016/j.probengmech.2018.03.004.

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In the BUS (Bayesian Updating with Structural reliability methods) approach, the uncertain parameter space is augmented by a uniform random variable and the Bayesian inference problem is interpreted as a structural reliability problem. A posterior sample is given by an augmented vector sample within the failure domain of the structural reliability problem where the realization of the uniform random variable is smaller than the likelihood function scaled by a constant c. The constant cc must be selected such that 1∕c is larger or equal than the maximum of the likelihood function, which, however, is typically unknown a-priori. For BUS combined with sampling based reliability methods, choosing c too small has a negative impact on the computational efficiency. To overcome the problem of selecting c, we propose a post-processing step for BUS that returns an unbiased estimate for the evidence and samples from the posterior distribution, even if 1∕c is selected smaller than the maximum of the likelihood function. The applicability of the proposed post-processing step is demonstrated by means of rejection sampling. However, it can be combined with any structural reliability method applied within the BUS framework.

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Additional Information:© 2018 Elsevier Ltd. Received 24 August 2017, Revised 25 January 2018, Accepted 29 March 2018, Available online 12 April 2018.
Subject Keywords:Bayesian updating; Bayesian model class selection; Rejection sampling; Structural reliability
Record Number:CaltechAUTHORS:20180412-155717120
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Official Citation:Wolfgang Betz, James L. Beck, Iason Papaioannou, Daniel Straub, Bayesian inference with reliability methods without knowing the maximum of the likelihood function, Probabilistic Engineering Mechanics, Volume 53, 2018, Pages 14-22, ISSN 0266-8920, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85798
Deposited By: Tony Diaz
Deposited On:13 Apr 2018 17:23
Last Modified:15 Nov 2021 20:32

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