Comparing prequential selection criteria for CIR and continuous-type spatio-temporal models for infectious disease data

Prequential analysis, although well-established from a theoretical point of view, has not been given the attention one would expect in practical applications. We investigate the advantages of one-step-ahead predictions for assessing model fit in a Bayesian framework. The methodology is applied to (sequential in nature) datasets of sheep pox and foot and mouth disease. Our count data on animal epidemics are especially suitable for this type of predictive approach due to their time ordering. The results indicate that a prequential approach in model assessment, although time consuming, improves model assessment in various directions, with most notational improvement being that the prequential approach respects the time ordering of the data.