Antithetic sampling for sequential Monte Carlo methods with application to state-space models
Antithetic sampling for sequential Monte Carlo methods with application to state-space models
复制标题
顺序蒙特卡罗方法的对偶采样及其在状态空间模型中的应用
DOI：
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复制
发表时间：
2015
影响因子：
1
通讯作者：
J. Olsson
中科院分区：
文献类型：
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作者：
Svetlana Bizjajeva;J. Olsson
在本文中，我们将标准蒙特卡罗模拟中广泛使用的对偶抽样的思想引入序贯蒙特卡罗方法的框架中。我们提出了一种标准辅助粒子过滤器的版本，其中粒子按块的方式突变，使得每个块内的所有粒子首先是共同祖先的后代，其次是在该祖先上有条件地负相关。通过对描述算法收敛的中心极限定理的弱极限的推导和检验，我们得出结论：当粒子滤波接近完全适应时，所产生的蒙特卡罗估计的渐近方差可以直接地减小，这涉及到所谓的最优方案核的逼近。作为说明，我们将该方法应用于状态空间模型的最优滤波。
In this paper, we cast the idea of antithetic sampling, widely used in standard Monte Carlo simulation, into the framework of sequential Monte Carlo methods. We propose a version of the standard auxiliary particle filter where the particles are mutated blockwise in such a way that all particles within each block are, first, offspring of a common ancestor and, second, negatively correlated conditionally on this ancestor. By deriving and examining the weak limit of a central limit theorem describing the convergence of the algorithm, we conclude that the asymptotic variance of the produced Monte Carlo estimates can be straightforwardly decreased by means of antithetic techniques when the particle filter is close to fully adapted, which involves approximation of the so-called optimal proposal kernel. As an illustration, we apply the method to optimal filtering in state-space models.
影响因子：
2.2
作者：
Julien Cornebise;É. Moulines;J. Olsson
通讯作者：
Julien Cornebise;É. Moulines;J. Olsson