Bayesian-optimal design via interacting particle systems

• 成果类型: Article
• 署名作者: Amzal, Billy; Bois, Frederic Y.; Parent, Eric; Robert, Christian R.
• 署名单位: Universite PSL; Universite Paris-Dauphine
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214505000001159
• 发表日期: 2006
• 页码: 773-785
• 关键词: population pharmacokinetics; caffeine; filter

摘要

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.