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Inference for SDE models via Approximate Bayesian Computation

Picchini, Umberto LU (2014) In Journal of Computational and Graphical Statistics 23(4). p.1080-1100
Abstract
Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard tool to model e.g. financial, neuronal and population growth dynamics. However inference for multidimensional SDE models is still very challenging, both computationally and theoretically. Approximate Bayesian computation (ABC) allow to perform Bayesian inference for models which are sufficiently complex that the likelihood function is either analytically unavailable or computationally prohibitive to evaluate. A computationally efficient ABC-MCMC algorithm is proposed, halving the running time in our... (More)
Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard tool to model e.g. financial, neuronal and population growth dynamics. However inference for multidimensional SDE models is still very challenging, both computationally and theoretically. Approximate Bayesian computation (ABC) allow to perform Bayesian inference for models which are sufficiently complex that the likelihood function is either analytically unavailable or computationally prohibitive to evaluate. A computationally efficient ABC-MCMC algorithm is proposed, halving the running time in our simulations. Focus is on the case where the SDE describes latent dynamics in state-space models; however the methodology is not limited to the state-space framework. Simulation studies for a pharmacokinetics/pharmacodynamics model and for stochastic chemical reactions are considered and a Matlab package implementing our ABC-MCMC algorithm is provided. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
early–rejection MCMC, likelihood-free inference, state-space model, stochastic differential equation, stochastic chemical reaction
in
Journal of Computational and Graphical Statistics
volume
23
issue
4
pages
1080 - 1100
publisher
American Statistical Association
external identifiers
  • wos:000343314300010
  • scopus:84908075115
ISSN
1537-2715
DOI
10.1080/10618600.2013.866048
language
English
LU publication?
yes
id
fe967cde-bb25-46e3-9134-8764fefab684 (old id 4215970)
date added to LUP
2014-01-31 20:08:38
date last changed
2017-10-05 11:16:40
@article{fe967cde-bb25-46e3-9134-8764fefab684,
  abstract     = {Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard tool to model e.g. financial, neuronal and population growth dynamics. However inference for multidimensional SDE models is still very challenging, both computationally and theoretically. Approximate Bayesian computation (ABC) allow to perform Bayesian inference for models which are sufficiently complex that the likelihood function is either analytically unavailable or computationally prohibitive to evaluate. A computationally efficient ABC-MCMC algorithm is proposed, halving the running time in our simulations. Focus is on the case where the SDE describes latent dynamics in state-space models; however the methodology is not limited to the state-space framework. Simulation studies for a pharmacokinetics/pharmacodynamics model and for stochastic chemical reactions are considered and a Matlab package implementing our ABC-MCMC algorithm is provided.},
  author       = {Picchini, Umberto},
  issn         = {1537-2715},
  keyword      = {early–rejection MCMC,likelihood-free inference,state-space model,stochastic differential equation,stochastic chemical reaction},
  language     = {eng},
  number       = {4},
  pages        = {1080--1100},
  publisher    = {American Statistical Association},
  series       = {Journal of Computational and Graphical Statistics},
  title        = {Inference for SDE models via Approximate Bayesian Computation},
  url          = {http://dx.doi.org/10.1080/10618600.2013.866048},
  volume       = {23},
  year         = {2014},
}