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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Bibliographic Details
Published in:Computational statistics & data analysis Vol. 52; no. 3; pp. 1674 - 1693
Main Authors: Golightly, A., Wilkinson, D.J.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 2008
Elsevier Science
Elsevier
Series:Computational Statistics & Data Analysis
Subjects:
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
Online Access:Get full text
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Description
Summary: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.
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ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2007.05.019