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@article{Beskos:2017:10.1017/apr.2016.77,
author = {Beskos, A and Crisan, D and Jasra, A and Kamatani, K and Zhou, Y},
doi = {10.1017/apr.2016.77},
journal = {Advances in Applied Probability},
pages = {24--48},
title = {A stable particle filter for a class of high-dimensional state-space models},
url = {http://dx.doi.org/10.1017/apr.2016.77},
volume = {49},
year = {2017}
}

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TY  - JOUR
AB  - We consider the numerical approximation of the filtering problem in high dimensions, thatis, when the hidden state lies in Rd with large d. For low-dimensional problems, one of themost popular numerical procedures for consistent inference is the class of approximationstermed particle filters or sequential Monte Carlo methods. However, in high dimensions,standard particle filters (e.g. the bootstrap particle filter) can have a cost that is exponentialin d for the algorithm to be stable in an appropriate sense. We develop a new particlefilter, called the space–time particle filter, for a specific family of state-space models indiscrete time. This new class of particle filters provides consistent Monte Carlo estimatesfor any fixed d, as do standard particle filters. Moreover, when there is a spatial mixingelement in the dimension of the state vector, the space–time particle filter will scale muchbetter with d than the standard filter for a class of filtering problems. We illustrate thisanalytically for a model of a simple independent and identically distributed structure anda model of an L-Markovian structure (L ≥ 1, L independent of d) in the d-dimensionalspace direction, when we show that the algorithm exhibits certain stability propertiesas d increases at a cost O(nN d2), where n is the time parameter and N is the numberof Monte Carlo samples, which are fixed and independent of d. Our theoretical resultsare also supported by numerical simulations on practical models of complex structures.The results suggest that it is indeed possible to tackle some high-dimensional filteringproblems using the space–time particle filter that standard particle filters cannot handle.
AU  - Beskos,A
AU  - Crisan,D
AU  - Jasra,A
AU  - Kamatani,K
AU  - Zhou,Y
DO  - 10.1017/apr.2016.77
EP  - 48
PY  - 2017///
SN  - 0001-8678
SP  - 24
TI  - A stable particle filter for a class of high-dimensional state-space models
T2  - Advances in Applied Probability
UR  - http://dx.doi.org/10.1017/apr.2016.77
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000399250500002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/49663
VL  - 49
ER  -

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