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We consider online prediction of a latent dynamic spatiotemporal process andestimation of the associated model parameters based on noisy data. The problemis motivated by the analysis of spatial data arriving in real-time and thecurrent parameter estimates and predictions are updated using the new data at afixed computational cost. Estimation and prediction is performed within anempirical Bayes framework with the aid of Markov chain Monte Carlo samples.Samples for the latent spatial field are generated using a sampling importanceresampling algorithm with a skewed-normal proposal and for the temporalparameters using Gibbs sampling with their full conditionals written in termsof sufficient quantities which are updated online. The spatial range parameteris estimated by a novel online implementation of an empirical Bayes method,called herein sequential empirical Bayes method. A simulation study shows thatour method gives similar results as an offline Bayesian method. We also findthat the skewed-normal proposal improves over the traditional Gaussianproposal. The application of our method is demonstrated for online monitoringof radiation after the Fukushima nuclear accident.

Sequential Empirical Bayes method for filtering dynamic spatiotemporal processes