Bayesian-Optimal Design via Interacting Particle Systems

Amzal, Billy; Bois, Frédéric Y.; Parent, Eric; Robert, Christian P.

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

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