A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Coupled conditional backward sampling particle filter (2020)

Lee, A., Singh, S. S., & Vihola, M. (2020). Coupled conditional backward sampling particle filter. Annals of Statistics, 48(5), 3066-3089. https://doi.org/10.1214/19-AOS1922

JYU-tekijät tai -toimittajat

Julkaisun tiedot

Julkaisun kaikki tekijät tai toimittajat: Lee, Anthony; Singh, Sumeetpal S.; Vihola, Matti

Lehti tai sarja: Annals of Statistics

ISSN: 0090-5364

eISSN: 2168-8966

Julkaisuvuosi: 2020

Volyymi: 48

Lehden numero: 5

Artikkelin sivunumerot: 3066-3089

Kustantaja: Institute of Mathematical Statistics

Julkaisumaa: Yhdysvallat (USA)

Julkaisun kieli: englanti

DOI: https://doi.org/10.1214/19-AOS1922

Julkaisun avoin saatavuus: Ei avoin

Julkaisukanavan avoin saatavuus: 

Julkaisu on rinnakkaistallennettu (JYX): https://jyx.jyu.fi/handle/123456789/71949

Julkaisu on rinnakkaistallennettu: https://arxiv.org/abs/1806.05852

Tiivistelmä

The conditional particle filter (CPF) is a promising algorithm for general hidden Markov model smoothing. Empirical evidence suggests that the variant of CPF with backward sampling (CBPF) performs well even with long time series. Previous theoretical results have not been able to demonstrate the improvement brought by backward sampling, whereas we provide rates showing that CBPF can remain effective with a fixed number of particles independent of the time horizon. Our result is based on analysis of a new coupling of two CBPFs, the coupled conditional backward sampling particle filter (CCBPF). We show that CCBPF has good stability properties in the sense that with fixed number of particles, the coupling time in terms of iterations increases only linearly with respect to the time horizon under a general (strong mixing) condition. The CCBPF is useful not only as a theoretical tool, but also as a practical method that allows for unbiased estimation of smoothing expectations, following the recent developments by Jacob, Lindsten and Schon (2020). Unbiased estimation has many advantages, such as enabling the construction of asymptotically exact confidence intervals and straightforward parallelisation.

YSO-asiasanat: Monte Carlo -menetelmät; stokastiset prosessit; Markovin ketjut; numeerinen analyysi

Vapaat asiasanat: backward sampling; convergence rate; coupling; conditional particle filter; unbiased

Liittyvät organisaatiot

Hankkeet, joissa julkaisu on tehty

OKM-raportointi: Kyllä

Raportointivuosi: 2020

JUFO-taso: 3