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Bayesian-Optimal Design via Interacting Particle Systems

Amzal, Billy; Bois, Frédéric Y.; Parent, Eric; Robert, Christian P. (2006), Bayesian-Optimal Design via Interacting Particle Systems, Journal of the American Statistical Association, 101, 474, p. 773-785. http://dx.doi.org/10.1198/016214505000001159

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Type
Article accepté pour publication ou publié
Date
2006
Journal name
Journal of the American Statistical Association
Volume
101
Number
474
Publisher
American Statistical Association
Pages
773-785
Publication identifier
http://dx.doi.org/10.1198/016214505000001159
Metadata
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Author(s)
Amzal, Billy
Bois, Frédéric Y.
Parent, Eric cc
Robert, Christian P.
Abstract (EN)
We propose a new stochastic algorithm for Bayesian-optimal design in nonlinear and high-dimensional contexts. Following Peter Müller, we solve an optimization problem by exploring the expected utility surface through Markov chain Monte Carlo simulations. The optimal design is the mode of this surface considered a probability distribution. Our algorithm relies on a “particle” method to efficiently explore high-dimensional multimodal surfaces, with simulated annealing to concentrate the samples near the modes. We first test the method on an optimal allocation problem for which the explicit solution is available, to compare its efficiency with a simpler algorithm. We then apply our method to a challenging medical case study in which an optimal protocol treatment needs to be determined. For this case, we propose a formalization of the problem in the framework of Bayesian decision theory, taking into account physicians' knowledge and motivations. We also briefly review further improvements and alternatives.
Subjects / Keywords
Bayesian decision theory; optimal design; MCMC; stochastic algorithm

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