期刊
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
卷 101, 期 474, 页码 773-785出版社
AMER STATISTICAL ASSOC
DOI: 10.1198/016214505000001159
关键词
Bayesian decision theory; experimental design; Markov chain Monte Carlo; particle methods; simulated annealing; Stochastic optimization
We propose a new stochastic algorithm for Bayesian-optimal design in nonlinear and high-dimensional contexts. Following Peter Muller, 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.
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