Using approximate Bayesian computation by Subset Simulation for efficient posterior assessment of dynamic state-space model classes
Journal article, 2018

Approximate Bayesian Computation (ABC) methods have gained in popularity over the last decade because they expand the horizon of Bayesian parameter inference methods to the range of models for which an analytical formula for the likelihood function might be difficult, or even impossible, to establish. The majority of the ABC methods rely on the choice of a set of summary statistics to reduce the dimension of the data. However, as has been noted in the ABC literature, the lack of convergence guarantees induced by the absence of a vector of sufficient summary statistics that assures intermodel sufficiency over the set of competing models hinders the use of the usual ABC methods when applied to Bayesian model selection or assessment. In this paper, we present a novel ABC model selection procedure for dynamical systems based on a recently introduced multilevel Markov chain Monte Carlo method, self-regulating ABC-SubSim, and a hierarchical state-space formulation of dynamic models. We show that this formulation makes it possible to independently approximate the model evidence required for assessing the posterior probability of each of the competing models. We also show that ABC-SubSim not only provides an estimate of the model evidence as a simple by-product but also gives the posterior probability of each model as a function of the tolerance level, which allows the ABC model choices made in previous studies to be understood. We illustrate the performance of the proposed framework for ABC model updating and model class selection by applying it to two problems in Bayesian system identification: a single-degree-of-freedom bilinear hysteretic oscillator and a three-story shear building with Masing hysteresis, both of which are subject to a seismic excitation.

Subset Simulation

System identification

Bayesian model selection

Bilinear

Approximate Bayesian Computation

Masing hysteretic models

Author

Majid Khorsand Vakilzadeh

Chalmers, Mechanics and Maritime Sciences, Dynamics

James L. Beck

California Institute of Technology (Caltech)

Thomas Abrahamsson

Chalmers, Mechanics and Maritime Sciences, Dynamics

SIAM Journal of Scientific Computing

1064-8275 (ISSN) 1095-7197 (eISSN)

Vol. 40 1 B168-B195

Subject Categories

Computer Engineering

Computational Mathematics

Computer Science

DOI

10.1137/16M1090466

More information

Latest update

4/13/2018