Sequential Bayesian inference for static parameters in dynamic state space models

TL;DR

This paper introduces a sequential Bayesian inference method for static parameters in dynamic state space models, leveraging grid-based posterior tracking and existing filtering techniques like Kalman filters, demonstrated across various models.

Contribution

It presents a novel grid-based approach for sequential inference of static parameters that integrates with existing filtering methods, applicable to diverse models.

Findings

Effective in linear Gaussian models

Comparable or superior to existing methods

Applicable to highly non-linear models

Abstract

A method for sequential Bayesian inference of the static parameters of a dynamic state space model is proposed. The method is based on the observation that many dynamic state space models have a relatively small number of static parameters (or hyper-parameters), so that in principle the posterior can be computed and stored on a discrete grid of practical size which can be tracked dynamically. Further to this, this approach is able to use any existing methodology which computes the filtering and prediction distributions of the state process. Kalman filter and its extensions to non-linear/non-Gaussian situations have been used in this paper. This is illustrated using several applications: linear Gaussian model, Binomial model, stochastic volatility model and the extremely non-linear univariate non-stationary growth model. Performance has been compared to both existing on-line method and off-line methods.