A hierarchical Bayesian space-time model for radioactivity deposition

A hierarchical Bayesian space-time (HBST) model, an extension of the class of dynamic linear models to space-time processes, is proposed for the statistical modelling of radioactivity deposition after a nuclear accident. It explicitly handles uncertainties associated with (i) predictions of depositions from a long-range atmospheric dispersal model, (ii) in-situ gamma ray measurements and (iii) spatial interpolations. Unlike existing environmental statistical models, the HBST model also accounts for an established food chain contamination model called ECOSYS for which it provides data assimilation capabilities. Three distinct formulations of the HBST model were applied to assimilate real data of radioactivity deposition from the Chernobyl accident in southern Germany. Two of those formulations differ on the functional form of their spatial covariance matrices while the third, a normal inverse-Wishart model, allows the spatial covariances to “learn” from data within the usual Bayesian paradigm. The later is shown to outperform the former models both in short and medium term forecasting as well as in a predictive interpolation test that took some measurements as out-of-sample.