TY - JOUR

T1 - Multilevel particle filters: normalizing constant estimation

AU - Jasra, Ajay

AU - Kamatani, Kengo

AU - Osei, Prince Peprah

AU - Zhou, Yan

N1 - Generated from Scopus record by KAUST IRTS on 2019-11-20

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://link.springer.com/10.1007/s11222-016-9715-5

UR - http://www.scopus.com/inward/record.url?scp=84994475251&partnerID=8YFLogxK

U2 - 10.1007/s11222-016-9715-5

DO - 10.1007/s11222-016-9715-5

M3 - Article

SN - 1573-1375

VL - 28

JO - Statistics and Computing

JF - Statistics and Computing

IS - 1

ER -