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首页> 外文期刊>Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability >Sequential Monte Carlo as approximate sampling: bounds, adaptive resampling via infinity-ESS, and an application to particle Gibbs
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Sequential Monte Carlo as approximate sampling: bounds, adaptive resampling via infinity-ESS, and an application to particle Gibbs

机译：顺序蒙特卡罗作为近似采样：界限，通过Infinity-ESS的自适应重采样，以及粒子吉布斯的应用

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摘要

Sequential Monte Carlo (SMC) algorithms were originally designed for estimating intractable conditional expectations within state-space models, but are now routinely used to generate approximate samples in the context of general-purpose Bayesian inference. In particular, SMC algorithms are often used as subroutines within larger Monte Carlo schemes, and in this context, the demands placed on SMC are different: control of mean-squared error is insufficient-one needs to control the divergence from the target distribution directly. Towards this goal, we introduce the conditional adaptive resampling particle filter, building on the work of Gordon, Salmond, and Smith (1993), Andrieu, Doucet, and Holenstein (2010), and Whiteley, Lee, and Heine (2016). By controlling a novel notion of effective sample size, the infinity-ESS, we establish the efficiency of the resulting SMC sampling algorithm, providing an adaptive resampling extension of the work of Andrieu, Lee, and Vihola (2018). We apply our results to arrive at new divergence bounds for SMC samplers with adaptive resampling as well as an adaptive resampling version of the Particle Gibbs algorithm with the same geometric-ergodicity guarantees as its nonadaptive counterpart.
机译：顺序蒙特卡罗（SMC）算法最初是为估算状态空间模型内的棘身条件期望而设计，但现在经常用于在通用贝叶斯推理的背景下产生近似样本。特别地，SMC算法通常用作较大的蒙特卡罗方案中的子程序，并且在此上下文中，对SMC的需求不同：平均误差的控制不足 - 一种需要直接控制目标分布的分歧。为了实现这一目标，我们介绍了有条件的自适应重采样粒子过滤器，建立了戈登，萨尔蒙德和史密斯（1993），安德鲁，杜培，霍恩斯坦（2010年），以及Whiteley，Lee和Heine（2016）。通过控制有效样本大小的新颖概念，无限-SES，我们建立了所得SMC采样算法的效率，提供Andrieu，Lee和Vihola（2018）的工作的适应性重采样扩展。我们将结果应用于具有自适应重采样的SMC采样器的新发散界，以及具有相同几何遍历性的粒子GIBBS算法的自适应重采样版本作为其非接受对应物。

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