Semi-complete data augmentation for efficient state space model fitting

Borowska, A. and King, R. (2023) Semi-complete data augmentation for efficient state space model fitting. Journal of Computational and Graphical Statistics, 32(1), pp. 19-35. (doi: 10.1080/10618600.2022.2077350)

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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 non-transferable 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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Borowska, Dr Agnieszka
Authors: Borowska, A., and King, R.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Journal of Computational and Graphical Statistics
Publisher:Taylor & Francis
ISSN (Online):1537-2715
Published Online:17 May 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in Journal of Computational and Graphical Statistics 32(1): 19-35
Publisher Policy:Reproduced under a Creative Commons License

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