Arnab Bhattacharya, Simon Wilson

This paper addresses the recursive Bayesian inference problem for a discrete time non-linear dynamic system commonly defined as a dynamic state-space model. This process evolves over time as a first order Markov process according to a transition density and the observations are assumed to be conditionally independent given the states and parameters. Bayes Law and the structure of the state-space model are used to sequentially update the posterior density of the model parameters as new observations arrive. In this talk various possible approximations are proposed and discussed that would allow fast functional approximation updates of the posterior distribution. These approximations rely on techniques such as the Kalman filter and its non-linear extensions, as well as the integrated nested Laplace approximation (Rue, Martino and Chopin, 2009). The approximate posterior is explored at a sufficient number of points on a grid which is computed at “good” evaluation points. The grid is re-assessed at each time point for addition/reduction of grid points. This new methodology of sequential updating makes the calculation of posterior both fast and accurate. It has been found to be extremely accurate for linear Gaussian models and it performance is also evaluated on several non-linear models.

**Keywords:** State space models; Kalman filter; Integrated nested Laplace approximation; Recursive updating

**Biography:** Mr. Bhattacharya is a Ph.D. student in the School of Computer Science and Statistics, Trinity College Dublin. He received his M.Sc. in statistics at the Indian Institute of Technology Kanpur in 2004, and has also worked for SAS. He will be submitting his Ph.D. later this year.