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Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models

Vakilzadeh, Majid K. and Huang, Yong and Beck, James L. and Abrahamsson, Thomas (2017) Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models. Mechanical Systems and Signal Processing, 84 . pp. 2-20. ISSN 0888-3270. https://resolver.caltech.edu/CaltechAUTHORS:20170104-092800219

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Abstract

A new multi-level Markov Chain Monte Carlo algorithm for Approximate Bayesian Computation, ABC-SubSim, has recently appeared that exploits the Subset Simulation method for efficient rare-event simulation. ABC-SubSim adaptively creates a nested decreasing sequence of data-approximating regions in the output space that correspond to increasingly closer approximations of the observed output vector in this output space. At each level, multiple samples of the model parameter vector are generated by a component-wise Metropolis algorithm so that the predicted output corresponding to each parameter value falls in the current data-approximating region. Theoretically, if continued to the limit, the sequence of data-approximating regions would converge on to the observed output vector and the approximate posterior distributions, which are conditional on the data-approximation region, would become exact, but this is not practically feasible. In this paper we study the performance of the ABC-SubSim algorithm for Bayesian updating of the parameters of dynamical systems using a general hierarchical state-space model. We note that the ABC methodology gives an approximate posterior distribution that actually corresponds to an exact posterior where a uniformly distributed combined measurement and modeling error is added. We also note that ABC algorithms have a problem with learning the uncertain error variances in a stochastic state-space model and so we treat them as nuisance parameters and analytically integrate them out of the posterior distribution. In addition, the statistical efficiency of the original ABC-SubSim algorithm is improved by developing a novel strategy to regulate the proposal variance for the component-wise Metropolis algorithm at each level. We demonstrate that Self-regulated ABC-SubSim is well suited for Bayesian system identification by first applying it successfully to model updating of a two degree-of-freedom linear structure for three cases: globally, locally and un-identifiable model classes, and then to model updating of a two degree-of-freedom nonlinear structure with Duffing nonlinearities in its interstory force-deflection relationship.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.ymssp.2016.02.024DOIArticle
http://www.sciencedirect.com/science/article/pii/S0888327016000753PublisherArticle
Additional Information:© 2016 Elsevier Ltd. Received 29 August 2015, Revised 6 February 2016, Accepted 13 February 2016, Available online 4 March 2016.
Subject Keywords:Approximate Bayesian Computation; Subset Simulation; Self-regulating ABC-SubSim algorithm; Optimal proposal variance scaling
Record Number:CaltechAUTHORS:20170104-092800219
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170104-092800219
Official Citation:Majid K. Vakilzadeh, Yong Huang, James L. Beck, Thomas Abrahamsson, Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models, Mechanical Systems and Signal Processing, Volume 84, Part B, 1 February 2017, Pages 2-20, ISSN 0888-3270, http://dx.doi.org/10.1016/j.ymssp.2016.02.024. (http://www.sciencedirect.com/science/article/pii/S0888327016000753)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73197
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:04 Jan 2017 18:04
Last Modified:03 Oct 2019 16:25

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