A Sequential Monte Carlo Algorithm to Incorporate Model Uncertainty in Bayesian Sequential Design
A Sequential Monte Carlo Algorithm to Incorporate Model Uncertainty in Bayesian Sequential Design
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DOI：
10.1080/10618600.2012.730083
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发表时间：
2014-03-01
影响因子：
2.4
通讯作者：
Pettitt, Anthony N.
中科院分区：
文献类型：
--
作者：
Drovandi, Christopher C.;McGree, James M.;Pettitt, Anthony N.
本文提出了一种顺序蒙特卡罗 (SMC) 算法，可用于在遇到离散数据时存在模型不确定性的情况下的任何一次性贝叶斯顺序设计问题。我们的重点是模型区分的自适应设计，但如果有不同的设计目标（例如参数估计或预测），则该方法也适用。 SMC 算法针对每个模型并行运行，该算法依赖于每个模型证据的方便估计器，该估计器本质上是重要性采样权重的函数。依赖求积来完成此任务的方法会受到维数灾难的影响。以这种方式近似后验模型概率使我们能够使用从信息论中导出的模型判别效用函数，这些函数以前很难计算（除了共轭模型之外）。该算法的一个主要优点是它几乎不需要针对特定问题进行调整。我们在三种应用中展示了该方法，包括区分患有运动神经元疾病的患者运动神经元数量下降的模型。运行其中一个示例的计算机代码作为在线补充材料提供。
This article presents a sequential Monte Carlo (SMC) algorithm that can be used for any one-at-a-time Bayesian sequential design problem in the presence of model uncertainty where discrete data are encountered. Our focus is on adaptive design for model discrimination but the methodology is applicable if one has a different design objective such as parameter estimation or prediction. An SMC algorithm is run in parallel for each model and the algorithm relies on a convenient estimator of the evidence of each model that is essentially a function of importance sampling weights. Methods that rely on quadrature for this task suffer from the curse of dimensionality. Approximating posterior model probabilities in this way allows us to use model discrimination utility functions derived from information theory that were previously difficult to compute except for conjugate models. A major benefit of the algorithm is that it requires very little problem-specific tuning. We demonstrate the methodology on three applications, including discriminating between models for decline in motor neuron numbers in patients suffering from motor neuron disease. Computer code to run one of the examples is provided as online supplementary materials.