A regularized bridge sampler for sparsely sampled diffusions
Lindström, Erik LU
(2012)
In Statistics and Computing
22(2).
p.615-623
- Abstract
- Sparsely sampled diffusion processes, in this paper interpreted as data sampled sparsely in time relative to the time constant, is a challenging statistical problem. Most approximations of the transition kernel are derived under the assumption that data is frequently sampled and these approximations are often severely biased for sparsely sampled data. Monte Carlo methods can be used for this problem as the transition density can be estimated with arbitrary accuracy regardless of the sampling frequency, but this is computationally expensive or even prohibited unless effective variance reduction is applied. The state of art variance reduction technique for diffusion processes is the Durham-Gallant (modified) bridge sampler. Their importance... (More)
- Sparsely sampled diffusion processes, in this paper interpreted as data sampled sparsely in time relative to the time constant, is a challenging statistical problem. Most approximations of the transition kernel are derived under the assumption that data is frequently sampled and these approximations are often severely biased for sparsely sampled data. Monte Carlo methods can be used for this problem as the transition density can be estimated with arbitrary accuracy regardless of the sampling frequency, but this is computationally expensive or even prohibited unless effective variance reduction is applied. The state of art variance reduction technique for diffusion processes is the Durham-Gallant (modified) bridge sampler. Their importance sampler is derived using a linearized, Gaussian approximation of the dynamics, and have proved successful for frequently sampled data. However, the approximation is often not valid for sparsely sampled data. We present a flexible, alternative derivation of the modified bridge sampler for multivariate, discretely observed diffusion models and modify it by taking uncertainty into account. The resulting sampler can be viewed as a combination of the basic sampler and the Durham-Gallant sampler, using the sampler that is most appropriate for the given problem, while still being computationally efficient. Our sampler is providing effective variance reduction for frequently and sparsely sampled data. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2278919
- author
- Lindström, Erik
LU
- organization
- publishing date
- 2012
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Bridge sampler, Time series, Diffusion processes, Monte Carlo methods, MCMC
- in
- Statistics and Computing
- volume
- 22
- issue
- 2
- pages
- 615 - 623
- publisher
- Springer
- external identifiers
-
- wos:000297543600020
- scopus:81955168104
- ISSN
- 0960-3174
- DOI
- 10.1007/s11222-011-9255-y
- language
- English
- LU publication?
- yes
- id
- a3bb540f-6d53-4f60-9c55-5dd9cf7d43d1 (old id 2278919)
- date added to LUP
- 2016-04-01 12:58:56
- date last changed
- 2022-01-27 08:40:25
@article{a3bb540f-6d53-4f60-9c55-5dd9cf7d43d1,
abstract = {{Sparsely sampled diffusion processes, in this paper interpreted as data sampled sparsely in time relative to the time constant, is a challenging statistical problem. Most approximations of the transition kernel are derived under the assumption that data is frequently sampled and these approximations are often severely biased for sparsely sampled data. Monte Carlo methods can be used for this problem as the transition density can be estimated with arbitrary accuracy regardless of the sampling frequency, but this is computationally expensive or even prohibited unless effective variance reduction is applied. The state of art variance reduction technique for diffusion processes is the Durham-Gallant (modified) bridge sampler. Their importance sampler is derived using a linearized, Gaussian approximation of the dynamics, and have proved successful for frequently sampled data. However, the approximation is often not valid for sparsely sampled data. We present a flexible, alternative derivation of the modified bridge sampler for multivariate, discretely observed diffusion models and modify it by taking uncertainty into account. The resulting sampler can be viewed as a combination of the basic sampler and the Durham-Gallant sampler, using the sampler that is most appropriate for the given problem, while still being computationally efficient. Our sampler is providing effective variance reduction for frequently and sparsely sampled data.}},
author = {{Lindström, Erik}},
issn = {{0960-3174}},
keywords = {{Bridge sampler; Time series; Diffusion processes; Monte Carlo methods; MCMC}},
language = {{eng}},
number = {{2}},
pages = {{615--623}},
publisher = {{Springer}},
series = {{Statistics and Computing}},
title = {{A regularized bridge sampler for sparsely sampled diffusions}},
url = {{http://dx.doi.org/10.1007/s11222-011-9255-y}},
doi = {{10.1007/s11222-011-9255-y}},
volume = {{22}},
year = {{2012}},
}