Multilevel particle filters: normalizing constant estimation

Ajay Jasra, Kengo Kamatani, Prince Peprah Osei, Yan Zhou

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

In this article, we introduce two new estimates of the normalizing constant (or marginal likelihood) for partially observed diffusion (POD) processes, with discrete observations. One estimate is biased but non-negative and the other is unbiased but not almost surely non-negative. Our method uses the multilevel particle filter of Jasra et al. (Multilevel particle lter, arXiv:1510.04977, 2015). We show that, under assumptions, for Euler discretized PODs and a given ε> 0 in order to obtain a mean square error (MSE) of O(ε2) one requires a work of O(ε- 2.5) for our new estimates versus a standard particle filter that requires a work of O(ε- 3). Our theoretical results are supported by numerical simulations.
Original languageEnglish (US)
JournalStatistics and Computing
Volume28
Issue number1
DOIs
StatePublished - Jan 1 2018
Externally publishedYes

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