论文标题
人口准蒙特卡洛
Population Quasi-Monte Carlo
论文作者
论文摘要
蒙特卡洛方法广泛用于近似于贝叶斯推断的复杂的多维积分。人口蒙特卡洛（PMC）是一类重要的蒙特卡洛方法，它利用一系列建议来生成近似目标分布的加权样品。通用PMC框架在三个步骤上进行了迭代：从一组建议中模拟样品，将权重分配给此类样品以纠正提案和目标分布之间的不匹配，然后通过从加权样品中重新采样来调整建议。当目标分布评估昂贵时，PMC具有其计算限制，因为收敛率为$ \ MATHCAL {O}（N^{ - 1/2}）$。为了解决这个问题，我们在本文中提出了一个新的人群准蒙特卡洛（PQMC）框架，该框架将准蒙特卡洛的想法集成到PMC的采样和适应步骤中。 PQMC中的主要新颖性是重要性支持点重新采样的想法，这是从加权建议样本中找到“最佳”子样本的确定性方法。此外，在PQMC框架内，我们为多元正常建议制定了有效的协方差适应策略。最后，为加权PMC估计器引入了一组新的校正权重，以提高标准PMC估计器的效率。我们证明了在广泛的数值模拟和摩擦钻孔应用中，PQMC超过PMC的经验收敛改善。
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 utilizes a population of proposals to generate weighted samples that approximate the target distribution. The generic PMC framework iterates over three steps: samples are simulated from a set of proposals, weights are assigned to such samples to correct for mismatch between the proposal and target distributions, and the proposals are then adapted via resampling from the weighted samples. When the target distribution is expensive to evaluate, the PMC has its computational limitation since the convergence rate is $\mathcal{O}(N^{-1/2})$. To address this, we propose in this paper a new Population Quasi-Monte Carlo (PQMC) framework, 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. Lastly, 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 convergence of PQMC over PMC in extensive numerical simulations and a friction drilling application.
