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

Majid Khorsand Vakilzadeh (Institutionen för tillämpad mekanik, Dynamik ; Svenskt VindkraftsTekniskt Centrum (SWPTC)) ; Yong Huang ; James L. Beck ; Thomas Abrahamsson (Institutionen för tillämpad mekanik, Dynamik ; Svenskt VindkraftsTekniskt Centrum (SWPTC))
Model Validation and Uncertainty Quantification vol 3. Conference Proceedings of the Society for Experimental Mechanics Series. 34th IMAC Conference and Exposition on Structural Dynamics, Orlando, Florida 25-28 jan 2016. (2191-5644). Vol. 3 (2016), p. 37-50.
[Konferensbidrag, refereegranskat]

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.

Nyckelord: Approximate Bayesian computation; Subset simulation; Adaptive modified Metropolis algorithm; Dynamical systems; Optimal proposal variance scaling

Denna post skapades 2016-08-06. Senast ändrad 2017-02-21.
CPL Pubid: 239869


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Institutioner (Chalmers)

Institutionen för tillämpad mekanik, Dynamik (1900-2017)
Svenskt VindkraftsTekniskt Centrum (SWPTC)



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