大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Central Limit Theorems for Coupled Particle Filters

Ajay Jasra (National University of Singapore)

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4. Central Limit Theorems for Coupled Particle Filters

大阪大学 数理・データ科学セミナー データ科学セミナーシリーズ 第37回

Central Limit Theorems for Coupled Particle Filters

Ajay Jasra (National University of Singapore)

In this talk we give new central limit theorems (CLT) for coupled particle filters (CPFs). CPFs are used for the sequential estimation of the difference of expectations w.r.t. 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 discretization $\Delta_l$ we show that the MCPF and the approach in Jasra et al (2018) have, under assumptions, an asymptotic variance that is upper-bounded by an expression that is (almost) $\mathcal{O}(\Delta_l)$, uniformly in time. The $\mathcal{O}(\Delta_l)$ rate 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).

本発表はJST CREST JPMJCR14D7によってサポートされています．