Sequential Bayesian inference for static parameters in dynamic state space models

摘要

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