Multilevel bootstrap particle filter

IF 1.5 2区数学 Q2 STATISTICS & PROBABILITY

Bernoulli Pub Date : 2021-04-16 DOI:10.3150/22-bej1468

K. Heine, D. Burrows

引用次数: 0

Abstract

We consider situations where the applicability of sequential Monte Carlo particle filters is compromised due to the expensive evaluation of the particle weights. To alleviate this problem, we propose a new particle filter algorithm based on the multilevel approach. We show that the resulting multilevel bootstrap particle filter (MLBPF) retains the strong law of large numbers as well as the central limit theorem of classical particle filters under mild conditions. Our numerical experiments demonstrate up to 85\% reduction in computation time compared to the classical bootstrap particle filter, in certain settings. While it should be acknowledged that this reduction is highly application dependent, and a similar gain should not be expected for all applications across the board, we believe that this substantial improvement in certain settings makes MLBPF an important addition to the family of sequential Monte Carlo methods.

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多级自举粒子滤波器

我们考虑的情况是，由于粒子权重的昂贵评估，顺序蒙特卡罗粒子滤波器的适用性受到损害。为了缓解这个问题，我们提出了一种新的基于多级方法的粒子滤波算法。我们证明了所得到的多级自举粒子滤波器（MLBPF）在温和条件下保留了强数定律以及经典粒子滤波器的中心极限定理。我们的数值实验表明，在某些设置下，与经典的自举粒子滤波器相比，计算时间减少了85%。虽然应该承认，这种减少高度依赖于应用程序，并且不应该期望所有应用程序都有类似的增益，但我们认为，在某些设置中的这种实质性改进使MLBPF成为序列蒙特卡罗方法家族的重要补充。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Bernoulli 数学-统计学与概率论

CiteScore

3.40

自引率

0.00%

发文量

116

审稿时长

6-12 weeks

期刊介绍： BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.