Semi-Complete Data Augmentation for Efficient State Space Model Fitting

Agnieszka Borowska*, Ruth King

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

We propose a novel efficient model-fitting algorithm for state space models. State space models are an intuitive and flexible class of models, frequently used due to the combination of their natural separation of the different mechanisms acting on the system of interest: the latent underlying system process; and the observation process. This flexibility, however, often comes at the price of more complicated model-fitting algorithms due to the associated analytically intractable likelihood. For the general case a Bayesian data augmentation approach is often employed, where the true unknown states are treated as auxiliary variables and imputed within the MCMC algorithm. However, standard “vanilla” MCMC algorithms may perform very poorly due to high correlation between the imputed states and/or parameters, often leading to model-specific bespoke algorithms being developed that are nontransferable to alternative models. The proposed method addresses the inefficiencies of traditional approaches by combining data augmentation with numerical integration in a Bayesian hybrid approach. This approach permits the use of standard “vanilla” updating algorithms that perform considerably better than the traditional approach in terms of improved mixing and lower autocorrelation, and has the potential to be incorporated into bespoke model-specific algorithms. To demonstrate the ideas, we apply our semi-complete data augmentation algorithm to different application areas and models, leading to distinct implementation schemes and improved mixing and demonstrating improved mixing of the model parameters. Supplementary materials for this article are available online.

Original languageEnglish
Pages (from-to)19-35
Number of pages17
JournalJournal of Computational and Graphical Statistics
Volume32
Issue number1
Early online date5 Jul 2022
DOIs
Publication statusPublished - 2 Jan 2023

Bibliographical note

Funding Information:
AB acknowledges funding from the UK Engineering and Physical Sciences Research Council (EPSRC), grant numbers EP/N014642/1, EP/R018634/1 and EP/T017899/1. RK was supported by the Leverhulme research fellowship RF-2019-299.

Publisher Copyright:
© 2022 The Author(s). Published with license by Taylor & Francis Group, LLC.

Funding

AB acknowledges funding from the UK Engineering and Physical Sciences Research Council (EPSRC), grant numbers EP/N014642/1, EP/R018634/1 and EP/T017899/1. RK was supported by the Leverhulme research fellowship RF-2019-299.

FundersFunder number
Engineering and Physical Sciences Research CouncilEP/T017899/1, EP/R018634/1, EP/N014642/1
Leverhulme TrustRF-2019-299

    Keywords

    • Bayesian inference
    • Data augmentation
    • Effective sample size
    • Markov chain Monte Carlo
    • Numerical integration

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