Variational Bayesian inference of linear state space models

Abstract

This article studies a variational Bayesian method to fix the linear regression (LR) model of which regressors are Gaussian distributed with non-zero prior means, and then apply the method to the linear state space (LSS) model. Here, we innovatively transform the LSS model into a special LR model: In each state, the value obtained from the predict step can be seen as the prior mean of the regressors, and the update step can be viewed as the iterative solving in LR model with non-zero prior means. We simulate the proposed algorithm with high-dimensional discrete LSS models where most states are prior zeros; simulation results show that the proposed algorithm and its applications in LSS are both effective and reliable.