Central limit theorem for sequential Monte Carlo methods and its application to bayesian inference
Central limit theorem for sequential Monte Carlo methods and its application to bayesian inference
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DOI：
10.1214/009053604000000698
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发表时间：
2004-12-01
影响因子：
4.5
通讯作者：
Chopin, N
中科院分区：
文献类型：
--
作者：
Chopin, N
术语“序列蒙特卡罗方法”或等效地“粒子滤波器”是指对给定序列的感兴趣分布（pi（t））执行蒙特卡罗近似的一般类别的迭代算法。本文建立了由这些计算方法产生的Monte Carlo估计的中心极限定理。该结果在对分布pi（t）的最小假设下成立，并且适用于包含文献中已经考虑的大多数序列Monte Carlo方法的一般框架，包括Gilks和Berzuini的重采样移动算法[J. R. Stat. Soc. Ser B Stat.美沙酮63（2001）127-146]和剩余再分配办法。相应的渐近方差提供了一个方便的测量精度的给定粒子滤波器。我们研究，特别是，在一些典型的例子贝叶斯应用程序，这些渐近方差是否和在哪个速率在时间上发散，以评估所考虑的算法的长期可靠性。
The term "sequential Monte Carlo methods" or, equivalently, "particle filters," refers to a general class of iterative algorithms that performs Monte Carlo approximations of a given sequence of distributions of interest (pi(t)). We establish in this paper a central limit theorem for the Monte Carlo estimates produced by these computational methods. This result holds under minimal assumptions on the distributions pi(t), and applies in a general framework which encompasses most of the sequential Monte Carlo methods that have been considered in the literature, including the resample-move algorithm of Gilks and Berzuini [J. R. Stat. Soc. Ser B Stat. Methodol. 63 (2001) 127-146] and the residual resampling scheme. The corresponding asymptotic variances provide a convenient measurement of the precision of a given particle filter. We study, in particular, in some typical examples of Bayesian applications, whether and at which rate these asymptotic variances diverge in time, in order to assess the long term reliability of the considered algorithm.