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Activity Number: 282 - Sampling and Ensembling in Statistical Computing
Type: Contributed
Date/Time: Tuesday, August 9, 2022 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Computing
Abstract #320975
Title: A Two-Stage Adaptive Metropolis Algorithm for Bayesian Calibration of Complex Computer Models
Author(s): Anirban Mondal*
Companies: Case Western Reserve University
Keywords: Markov chain Monte Carlo; Adaptive Metropolis; Two-stage Metropolis-Hasings; Bayesian model calibration; Ergodicity; Computer models
Abstract:

We propose a new sampling algorithm combining two quite powerful ideas in the Markov chain Monte Carlo literature - adaptive Metropolis sampler and two-stage Metropolis-Hastings sampler. The proposed sampling method is particularly very useful for high-dimensional posterior sampling in Bayesian model calibration which involves a computationally expensive forward model. In the first stage of the algorithm, an adaptive proposal is used based on the previously sampled states, and the corresponding acceptance probability is computed based on an approximated posterior involving an inexpensive surrogate model. The expensive target posterior using the true forward model is evaluated in the second stage only if the proposal is accepted in the inexpensive first stage. While the adaptive nature of the algorithm guarantees faster convergence of the chain and very good mixing properties, the two-stage approach helps in rejecting the bad proposals in the inexpensive first stage, making the algorithm computationally efficient. As the proposals are dependent on the previous states the chain loses its Markov property, but we prove that it retains the desired ergodicity property.


Authors who are presenting talks have a * after their name.

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