May 2023 Efficient Data Augmentation Techniques for Some Classes of State Space Models
Linda S. L. Tan
Author Affiliations +
Statist. Sci. 38(2): 240-261 (May 2023). DOI: 10.1214/22-STS867


Data augmentation improves the convergence of iterative algorithms, such as the EM algorithm and Gibbs sampler by introducing carefully designed latent variables. In this article, we first propose a data augmentation scheme for the first-order autoregression plus noise model, where optimal values of working parameters introduced for recentering and rescaling of the latent states, can be derived analytically by minimizing the fraction of missing information in the EM algorithm. The proposed data augmentation scheme is then utilized to design efficient Markov chain Monte Carlo (MCMC) algorithms for Bayesian inference of some non-Gaussian and nonlinear state space models, via a mixture of normals approximation coupled with a block-specific reparametrization strategy. Applications on simulated and benchmark real data sets indicate that the proposed MCMC sampler can yield improvements in simulation efficiency compared with centering, noncentering and even the ancillarity-sufficiency interweaving strategy.

Funding Statement

The author was supported by the start-up grant R-155-000-190-133.


The author would like to thank the Editor, Associate Editor and three referees for their comments and helpful suggestions, which have improved this manuscript greatly. The author also wishes to thank Dion Kwan and Robert Kohn for comments and discussion on this work.


Download Citation

Linda S. L. Tan. "Efficient Data Augmentation Techniques for Some Classes of State Space Models." Statist. Sci. 38 (2) 240 - 261, May 2023.


Published: May 2023
First available in Project Euclid: 28 October 2022

MathSciNet: MR4596758
zbMATH: 07708430
Digital Object Identifier: 10.1214/22-STS867

Keywords: ancillarity-sufficiency interweaving strategy , Data augmentation , EM algorithm , Markov chain Monte Carlo , reparametrization , state space model , stochastic volatility model

Rights: Copyright © 2023 Institute of Mathematical Statistics


This article is only available to subscribers.
It is not available for individual sale.

Vol.38 • No. 2 • May 2023
Back to Top