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.
Identifying the Optimal Integration Time in Hamiltonian Monte Carlo
通过利用光滑概率系统的自然几何结构，哈密顿蒙特卡罗产生计算效率高的马尔可夫链蒙特卡罗估计。至少在算法足够好的情况下。在本文中，我将展示如何几何基础的哈密顿蒙特卡罗隐含地确定这些参数的最佳选择，特别是积分时间。然后，我认为这些原则在现有的算法和一个新的实现称为\emph{Exhaustive Hamiltonian Monte Carlo}的实际后果，然后在一些说明性的例子证明这些想法的效用。
Some Contributions to Sequential Monte Carlo Methods for Option Pricing
期权定价是金融工程中的一个重要问题。在许多具有实际意义的场景中，与标的资产相关的金融期权价格简化为计算w.r.t.~扩散过程。一般来说，这些期望值无法通过分析计算，而近似这些数量的一种方法是通过蒙特卡罗方法;蒙特卡罗方法至少从20世纪70年代开始就被用于期权定价。在Del Moral，P.\& Shevchenko，P.V.（2014）"Valuation of barrier options using序贯蒙特卡罗"和Jasra，A. \& Del Moral，P.（2011）"期权定价的序贯蒙特卡罗"，序贯蒙特卡罗（SMC）方法是应用于这种情况的自然工具，可以大大改善标准蒙特卡罗。在本文中，本着类似的精神，Del Moral，P.\& Shevchenko，P.V.（2014）"Valuation of barrier options using序贯蒙特卡罗"和Jasra，A. \& Del Moral，P.（2011）"期权定价的序贯蒙特卡罗"我们表明，通过构建一系列人工目标密度随时间的推移使用SMC方法可以实现显着收益。特别是，我们近似的最佳重要性抽样分布的SMC算法，通过使用一系列的加权函数。这是证明了两个例子，障碍期权和目标应计赎回票据（TARN的）。我们还提供了我们的SMC估计的无偏性的证明。
