Sequential Empirical Bayes method for filtering dynamic spatiotemporal processes

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. We use a resampling algorithm based on a skewed-normal-corrected proposal density for the prediction step which is shown to improve over the traditional Gaussian proposal. The associated spatial correlation matrix is estimated by a novel online implementation of an empirical Bayes method, called herein sequential empirical Bayes method. A simulation study shows that our method has many advantages in terms of accuracy and Monte Carlo efficiency. The application of our method is demonstrated for online monitoring of radiation after the Fukushima nuclear accident.