Augmented pseudo-marginal Metropolis–Hastings for partially observed diffusion processes

We consider the problem of inference for nonlinear, multivariate diffusion processes, satisfying Itô stochastic differential equations (SDEs), using data at discrete times that may be incomplete and subject to measurement error. Our starting point is a state-of-the-art correlated pseudo-marginal Met...

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Bibliographic Details
Published inStatistics and computing Vol. 32; no. 1
Main Authors Golightly, Andrew, Sherlock, Chris
Format Journal Article
LanguageEnglish
Published New York Springer US 15.02.2022
Springer Nature B.V
Subjects
Algorithms
Artificial Intelligence
Computer Science
Differential equations
Diffusion
Error analysis
Inference
Probability and Statistics in Computer Science
Resampling
Statistical Theory and Methods
Statistics and Computing/Statistics Programs
Linear noise approximation
Data augmentation
Pseudo-marginal Metropolis–Hastings
Bayesian inference
Stochastic differential equation
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ISSN0960-3174
1573-1375
1573-1375
DOI10.1007/s11222-022-10083-5

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Summary:We consider the problem of inference for nonlinear, multivariate diffusion processes, satisfying Itô stochastic differential equations (SDEs), using data at discrete times that may be incomplete and subject to measurement error. Our starting point is a state-of-the-art correlated pseudo-marginal Metropolis–Hastings algorithm, that uses correlated particle filters to induce strong and positive correlation between successive likelihood estimates. However, unless the measurement error or the dimension of the SDE is small, correlation can be eroded by the resampling steps in the particle filter. We therefore propose a novel augmentation scheme, that allows for conditioning on values of the latent process at the observation times, completely avoiding the need for resampling steps. We integrate over the uncertainty at the observation times with an additional Gibbs step. Connections between the resulting pseudo-marginal scheme and existing inference schemes for diffusion processes are made, giving a unified inference framework that encompasses Gibbs sampling and pseudo marginal schemes. The methodology is applied in three examples of increasing complexity. We find that our approach offers substantial increases in overall efficiency, compared to competing methods
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ISSN:0960-3174
1573-1375
1573-1375
DOI:10.1007/s11222-022-10083-5