Bayesian-optimal design via interacting particle systems
Bayesian-optimal design via interacting particle systems
复制标题
DOI：
10.1198/016214505000001159
复制
发表时间：
2006-06-01
影响因子：
3.7
通讯作者：
Robert, Christian R.
中科院分区：
文献类型：
--
作者：
Amzal, Billy;Bois, Frederic Y.;Robert, Christian R.
提出了一种新的非线性高维贝叶斯最优设计的随机算法。在Peter Muller之后，我们通过马尔可夫链蒙特卡罗模拟探索期望效用面来解决优化问题。最优设计是将该曲面的模式视为概率分布。我们的算法依赖于一个“粒子”的方法来有效地探索高维多峰表面，模拟退火集中的模式附近的样本。首先，我们测试的方法上的最优分配问题的显式解决方案是可用的，比较其效率与一个更简单的算法。然后，我们将我们的方法应用于一个具有挑战性的医疗案例研究，其中需要确定最佳的协议治疗。对于这种情况下，我们提出了一个形式化的贝叶斯决策理论的框架内的问题，考虑到医生的知识和动机。我们还简要回顾了进一步的改进和替代方案。
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.