Efficient data augmentation techniques for some classes of state space models

TL;DR

This paper introduces optimized data augmentation methods for certain state space models, enhancing the efficiency of Bayesian inference algorithms like MCMC by analytically deriving optimal parameters and employing mixture approximations.

Contribution

It proposes a novel data augmentation scheme for autoregressive models and develops efficient MCMC algorithms for non-Gaussian, nonlinear state space models, improving computational performance.

Findings

Improved MCMC efficiency over existing strategies

Analytical derivation of optimal working parameters

Successful application to real and simulated datasets

Abstract

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 datasets indicate that the proposed MCMC sampler can yield improvements in simulation efficiency compared with centering, noncentering and even the ancillarity-sufficiency interweaving strategy.