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A sequential Monte Carlo algorithm to incorporate model uncertainty in Bayesian sequential design

Drovandi, Christopher C., McGree, James, & Pettitt, Anthony N. (2014) A sequential Monte Carlo algorithm to incorporate model uncertainty in Bayesian sequential design. Journal of Computational and Graphical Statistics, 23(1), pp. 3-24.

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Abstract

Here we present a sequential Monte Carlo (SMC) algorithm that can be used for any one-at-a-time Bayesian sequential design problem in the presence of model uncertainty where discrete data are encountered. Our focus is on adaptive design for model discrimination but the methodology is applicable if one has a different design objective such as parameter estimation or prediction. An SMC algorithm is run in parallel for each model and the algorithm relies on a convenient estimator of the evidence of each model which is essentially a function of importance sampling weights. Other methods for this task such as quadrature, often used in design, suffer from the curse of dimensionality. Approximating posterior model probabilities in this way allows us to use model discrimination utility functions derived from information theory that were previously difficult to compute except for conjugate models. A major benefit of the algorithm is that it requires very little problem specific tuning. We demonstrate the methodology on three applications, including discriminating between models for decline in motor neuron numbers in patients suffering from neurological diseases such as Motor Neuron disease.

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ID Code: 49601
Item Type: Journal Article
Additional URLs:
Keywords: Entropy, Model discrimination, Mutual information, Optimal design
DOI: 10.1080/10618600.2012.730083
ISSN: 1537-2715
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2014 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America
Deposited On: 11 Apr 2012 09:12
Last Modified: 06 Apr 2014 20:50

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