A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

McGree, James, Drovandi, Christopher C., White, Gentry, & Pettitt, Anthony N. (2016) A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design. Statistics and Computing, 26(5), pp. 1121-1136.

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A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.

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ID Code: 77732
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: Importance Sampling, Laplace approximation, Nonlinear regression, Optimal design, Parallel computing, Particle filter, Quasi Monte Carlo
DOI: 10.1007/s11222-015-9596-z
ISSN: 1573-1375
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400)
Divisions: Current > Research Centres > ARC Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS)
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2015 Springer
Deposited On: 16 Oct 2014 00:02
Last Modified: 05 May 2017 05:54

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