Online filtering and estimation for dynamic spatiotemporal processes based on exponential family data

We consider online prediction of a latent dynamic spatiotemporal process and estimation of the associated model parameters based on noisy data. The problem is motivated by the analysis of spatial data arriving in real-time and the current parameter estimates and predictions are updated using the new data at a fixed computational cost. Estimation and prediction is performed within an Empirical Bayes framework with the aid of Markov chain Monte Carlo samples. For the prediction we employ a resampling algorithm based on a skewed normal proposal density. Some of the model parameters are estimated by incorporating the aforementioned resampling algorithm within a Gibbs sampler and updating certain sufficient statistics. These sufficient statistics depend on the spatial correlation matrix which is estimated by a novel online implementation of an empirical Bayes method using the samples drawn by the proposed algorithm. Theoretical and simulation results verify the accuracy of our approach. Our method is also used for analyzing the dynamic spatiotemporal concentration of radioactive material caused after the Fukushima's power plant station accident in 2011.