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Particle-based likelihood inference in partially observed diffusion processes using generalised Poisson estimators

Olsson, Jimmy LU and Ströjby, Jonas LU (2011) In Electronic Journal of Statistics 5. p.1090-1122
Abstract
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form expressions of the transition densities. Thus, in order to estimate efficiently the EM intermediate quantity we construct, using novel techniques for unbiased estimation of diffusion transition densities, a random weight fixed-lag auxiliary particle smoother, which avoids the well known problem of particle trajectory degeneracy in the smoothing mode. The estimator is justified theoretically and demonstrated on a simulated example.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Auxiliary particle filter, EM algorithm, exact algorithm, generalised, Poisson estimator, partially observed diffusion process, sequential, Monte Carlo
in
Electronic Journal of Statistics
volume
5
pages
1090 - 1122
publisher
Institute of Mathematical Statistics
external identifiers
  • wos:000295324700001
  • scopus:84859831900
ISSN
1935-7524
DOI
10.1214/11-EJS632
language
English
LU publication?
yes
id
5ad4ab8f-f7da-4cc7-b80c-5cd2583e32de (old id 2179491)
date added to LUP
2011-10-25 10:56:31
date last changed
2017-04-09 03:57:20
@article{5ad4ab8f-f7da-4cc7-b80c-5cd2583e32de,
  abstract     = {This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form expressions of the transition densities. Thus, in order to estimate efficiently the EM intermediate quantity we construct, using novel techniques for unbiased estimation of diffusion transition densities, a random weight fixed-lag auxiliary particle smoother, which avoids the well known problem of particle trajectory degeneracy in the smoothing mode. The estimator is justified theoretically and demonstrated on a simulated example.},
  author       = {Olsson, Jimmy and Ströjby, Jonas},
  issn         = {1935-7524},
  keyword      = {Auxiliary particle filter,EM algorithm,exact algorithm,generalised,Poisson estimator,partially observed diffusion process,sequential,Monte Carlo},
  language     = {eng},
  pages        = {1090--1122},
  publisher    = {Institute of Mathematical Statistics},
  series       = {Electronic Journal of Statistics},
  title        = {Particle-based likelihood inference in partially observed diffusion processes using generalised Poisson estimators},
  url          = {http://dx.doi.org/10.1214/11-EJS632},
  volume       = {5},
  year         = {2011},
}