Bayesian inference for nonlinear multivariate diffusion models observed with error

Diffusion processes governed by stochastic differential equations (SDEs) are a well-established tool for modelling continuous time data from a wide range of areas. Consequently, techniques have been developed to estimate diffusion parameters from partial and discrete observations. Likelihood-based i...

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Vydáno v:	Computational statistics & data analysis Ročník 52; číslo 3; s. 1674 - 1693
Hlavní autoři:	Golightly, A., Wilkinson, D.J.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 2008 Elsevier Science Elsevier
Edice:	Computational Statistics & Data Analysis
Témata:	Bayesian inference Exact sciences and technology General topics Innovation scheme Mathematics MCMC Multivariate analysis Nonlinear stochastic differential equation Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Parametric inference Particle filter Probability and statistics Reparameterisation Sciences and techniques of general use Statistics MCMC Nonlinear stochastic differential equation Innovation scheme Bayesian inference Reparameterisation Particle filter Density estimation Parameter estimation Mixing Statistical distribution Error estimation Differential equation Continuous time Multivariate analysis Stochastic method Stochastic process Markov chain Distribution function Diffusion process Integral equation Approximation theory Latent value Measurement error Posterior distribution Stochastic equation Bayes estimation Mixed distribution Monte Carlo method Data analysis Approximation Discrete data Statistical estimation Numerical analysis Statistical computation Non linear model
ISSN:	0167-9473, 1872-7352
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Popis
Shrnutí:	Diffusion processes governed by stochastic differential equations (SDEs) are a well-established tool for modelling continuous time data from a wide range of areas. Consequently, techniques have been developed to estimate diffusion parameters from partial and discrete observations. Likelihood-based inference can be problematic as closed form transition densities are rarely available. One widely used solution involves the introduction of latent data points between every pair of observations to allow a Euler–Maruyama approximation of the true transition densities to become accurate. In recent literature, Markov chain Monte Carlo (MCMC) methods have been used to sample the posterior distribution of latent data and model parameters; however, naive schemes suffer from a mixing problem that worsens with the degree of augmentation. A global MCMC scheme that can be applied to a large class of diffusions and whose performance is not adversely affected by the number of latent values is therefore explored. The methodology is illustrated by estimating parameters governing an auto-regulatory gene network, using partial and discrete data that are subject to measurement error.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	0167-9473 1872-7352
DOI:	10.1016/j.csda.2007.05.019