Central Limit Theorems for Coupled Particle Filters

Jasra, Ajay; Yu, Fangyuan

Central Limit Theorems for Coupled Particle Filters

Files

coupl_clt.pdf (573.8 KB)

Type

Article

Authors

Jasra, Ajay

Yu, Fangyuan

KAUST Department

Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Statistics

KAUST Grant Number

KAUST Competitive Research Grants Program-Round 4 (CRG4) project, Advanced Multi-Level sampling techniques for Bayesian Inverse Problems with applications to subsurface, ref: 2584

Preprint Posting Date

2018-10-11

Date

2020-09-24

Abstract

In this article we prove new central limit theorems (CLTs) for several coupled particle filters (CPFs). CPFs are used for the sequential estimation of the difference of expectations with respect to filters which are in some sense close. Examples include the estimation of the filtering distribution associated to different parameters (finite difference estimation) and filters associated to partially observed discretized diffusion processes (PODDP) and the implementation of the multilevel Monte Carlo (MLMC) identity. We develop new theory for CPFs, and based upon several results, we propose a new CPF which approximates the maximal coupling (MCPF) of a pair of predictor distributions. In the context of ML estimation associated to PODDP with time-discretization, we show that the MCPF and the approach of Jasra, Ballesio, et al. (2018) have, under certain assumptions, an asymptotic variance that is bounded above by an expression that is of (almost) the order of , uniformly in time. The bound preserves the so-called forward rate of the diffusion in some scenarios, which is not the case for the CPF in Jasra et al. (2017).

Citation

Jasra, A., & Yu, F. (2020). Central limit theorems for coupled particle filters. Advances in Applied Probability, 52(3), 942–1001. doi:10.1017/apr.2020.27

Acknowledgements

AJ & FY were supported by KAUST baseline funding. AJ was supported under the KAUST Competitive Research Grants Program-Round 4 (CRG4) project, Advanced Multi-Level sampling techniques for Bayesian Inverse Problems with applications to subsurface, ref: 2584. We would like to thank Alexandros Beskos, Sumeetpal Singh and Xin Tong for useful conversations associated to this work. We thank two referees, the associate editor and editor in chief for substantial comments which have lead to an improvement of the article.

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