Population Quasi-Monte Carlo
Population Quasi-Monte Carlo
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DOI：
10.1080/10618600.2022.2034637
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发表时间：
2020-12
影响因子：
2.4
通讯作者：
Chaofan Huang;V. Roshan;Joseph H. Milton;Simon Mak
中科院分区：
文献类型：
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作者：
Chaofan Huang;V. Roshan;Joseph H. Milton;Simon Mak
摘要蒙特卡罗方法被广泛用于贝叶斯推理中的复杂多维积分近似。群体蒙特卡罗（PMC）方法是一类重要的蒙特卡罗方法，它通过调整一个群体的建议来产生近似于目标分布的加权样本。当目标分布的评估成本很高时，PMC可能会遇到计算限制，因为它需要对目标分布进行多次评估。为了解决这个问题，我们提出了一种新方法，即群体拟蒙特卡罗（PQMC），它将拟蒙特卡罗思想集成到PMC的采样和自适应步骤中。PQMC中的一个关键新奇之处是重要性支持点恢复的想法，这是一种确定性方法，用于从加权提案样本中找到“最佳”子样本。此外，在PQMC框架内，我们开发了一个有效的协方差自适应策略的多元正态建议。最后，一组新的校正权重的加权PMC估计，以提高效率，从标准PMC估计。我们证明了改进的经验性能PQMC PMC在广泛的数值模拟和摩擦钻井应用。本文的补充材料可在网上查阅。
Abstract Monte Carlo methods are widely used for approximating complicated, multidimensional integrals for Bayesian inference. Population Monte Carlo (PMC) is an important class of Monte Carlo methods, which adapts a population of proposals to generate weighted samples that approximate the target distribution. When the target distribution is expensive to evaluate, PMC may encounter computational limitations since it requires many evaluations of the target distribution. To address this, we propose a new method, Population Quasi-Monte Carlo (PQMC), which integrates Quasi-Monte Carlo ideas within the sampling and adaptation steps of PMC. A key novelty in PQMC is the idea of importance support points resampling, a deterministic method for finding an “optimal” subsample from the weighted proposal samples. Moreover, within the PQMC framework, we develop an efficient covariance adaptation strategy for multivariate normal proposals. Finally, a new set of correction weights is introduced for the weighted PMC estimator to improve the efficiency from the standard PMC estimator. We demonstrate the improved empirical performance of PQMC over PMC in extensive numerical simulations and a friction drilling application. Supplementary materials for this article are available online.