Bayesian sequential parameter estimation

A new approach of sequential parameter learning is proposed for a special general class of state-space model where the state equation is linear with Gaussian noise. In this approach, the filtering density of the state variable and unknown parameters is jointly and iteratively approximated by either Gaussian density or mixture Gaussian density. Compared to particle-based solutions, it is believed to be more robust to outlier and the traditional degeneracy problem due to the smooth functional approximation. Furthermore, this approach does not rely on the availability of sufficient statistics as in some recent particle-based parameter learning methods, and hence can be applied into different modelling classes. The approach is implemented in different variants, based on iterative Laplace approximation (iterLap, Bornkamp, 2011a), importance sampling (IS) and expectation-maximization (EM), and then analysed in various examples.