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A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

机译：贝叶斯顺序设计中随机效应模型的伪边际顺序蒙特卡洛算法

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摘要

Motivated by the need to sequentially design experiments for the collection of data in batches or blocks, a new pseudo-marginal sequential Monte Carlo algorithm is proposed for random effects models where the likelihood is not analytic, and has to be approximated. This new algorithm is an extension of the idealised sequential Monte Carlo algorithm where we propose to unbiasedly approximate the likelihood to yield an efficient exact-approximate algorithm to perform inference and make decisions within Bayesian sequential design. We propose four approaches to unbiasedly approximate the likelihood: standard Monte Carlo integration; randomised quasi-Monte Carlo integration, Laplace importance sampling and a combination of Laplace importance sampling and randomised quasi-Monte Carlo. These four methods are compared in terms of the estimates of likelihood weights and in the selection of the optimal sequential designs in an important pharmacological study related to the treatment of critically ill patients. As the approaches considered to approximate the likelihood can be computationally expensive, we exploit parallel computational architectures to ensure designs are derived in a timely manner.
机译：由于需要顺序设计实验以批量或块状地收集数据，因此提出了一种新的伪边际顺序蒙特卡洛算法，用于随机效应模型，这种模型无法分析似然性，必须对其进行近似估计。这种新算法是理想化顺序蒙特卡洛算法的扩展，在该算法中，我们提出了无偏近似的可能性，以产生有效的精确近似算法来执行推理并在贝叶斯序列设计中做出决策。我们提出了四种方法来无偏地近似该可能性：标准蒙特卡洛积分；随机拟蒙特卡洛积分，拉普拉斯重要性抽样以及拉普拉斯重要性抽样与随机拟蒙特卡洛的组合。在与重症患者治疗相关的一项重要药理研究中，根据可能性权重的估计以及最佳顺序设计的选择对这四种方法进行了比较。由于考虑到近似可能性的方法在计算上可能会非常昂贵，因此我们采用并行计算体系结构来确保及时获得设计。

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