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Approximate Bayesian Computation by Subset Simulation for Parameter Inference of Dynamical Models

Vakilzadeh, Majid K. and Huang, Yong and Beck, James L. and Abrahamsson, Thomas (2016) Approximate Bayesian Computation by Subset Simulation for Parameter Inference of Dynamical Models. In: Model Validation and Uncertainty Quantification. Conference Proceedings of the Society for Experimental Mechanics Series. Vol.3. Springer , pp. 37-50. ISBN 978-3-319-29753-8.

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A new multi-level Markov chain Monte Carlo algorithm for Bayesian inference, ABC-SubSim, has recently appeared that combines the principles of Approximate Bayesian Computation (ABC) with the method of subset simulation for efficient rare-event simulation. ABC-SubSim adaptively creates a nested decreasing sequence of data-approximating regions in the output space. This sequence corresponds to increasingly closer approximations of the observed output vector in this output space. At each stage, the approximate likelihood function at a given value of the model parameter vector is defined as the probability that the predicted output corresponding to that parameter value falls in the current data-approximating region. If continued to the limit, the sequence of the data-approximating regions would converge on to the observed output vector and the approximate likelihood function would become exact, but this is not computationally feasible. At the heart of this paper is the interpretation of the resulting approximate likelihood function. We show that under the assumption of the existence of uniformly-distributed measurement errors, ABC gives exact Bayesian inference. Moreover, we present a new optimal proposal variance scaling strategy which enables ABC-SubSim to efficiently explore the posterior PDF. The algorithm is applied to the model updating of a two degree-of-freedom linear structure to illustrate its ability to handle model classes with various degrees of identifiability.

Item Type:Book Section
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Huang, Yong0000-0002-7963-0720
Additional Information:© 2016 The Society for Experimental Mechanics, Inc. First Online: 28 June 2016. The first author of this paper wants to express his gratitude to the California Institute of Technology (Caltech) for kindly hosting him during the course of this work.
Subject Keywords:Approximate Bayesian computation – Subset simulation – Adaptive modified Metropolis algorithm – Dynamical systems – Optimal proposal variance scaling
Series Name:Conference Proceedings of the Society for Experimental Mechanics Series
Record Number:CaltechAUTHORS:20170105-085153114
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73256
Deposited By: Tony Diaz
Deposited On:05 Jan 2017 17:45
Last Modified:11 Nov 2021 05:13

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