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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)
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author
organization
publishing date
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
2012-01-11 13:33:38
date last changed
2017-05-28 03:52:05
@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},
  keyword      = {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},
  volume       = {22},
  year         = {2012},
}