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

Golightly, Andrew; Sherlock, Chris

Abstract

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.

Citation

Golightly, A., & Sherlock, C. (2022). Augmented pseudo-marginal Metropolis-Hastings for partially observed diffusion processes. Statistics and Computing, 32, Article 21. https://doi.org/10.1007/s11222-022-10083-5

• Journal Article Type: Article
• Acceptance Date: Jan 21, 2022
• Online Publication Date: Feb 15, 2022
• Publication Date: 2022-02
• Deposit Date: Feb 9, 2022
• Publicly Available Date: Apr 6, 2022
• Journal: Statistics and Computing
• Print ISSN: 0960-3174
• Electronic ISSN: 1573-1375
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 32
• Article Number: 21
• DOI: https://doi.org/10.1007/s11222-022-10083-5
• Related Public URLs: https://arxiv.org/pdf/2009.05318.pdf