Bayesian Model Monitoring

Abstract

SUMMARY A simple method of monitoring the predictive performance of a class of Bayesian models is introduced. The models involve sequential analyses of sequences of observations and are appropriate for a variety of monitoring and forecasting applications. For any given model, the monitoring technique is based on a comparison of the predictive ability of the model, measured by the observed values of predictive densities, with that of a single alternative. The alternative is constructed sequentially and is designed, for the class of models considered, as a relatively general yet neutral alternative to the original. The monitor is used as a general diagnostic tool to detect and assess discrepancies between the data and predictions generated from the model; particular sources of such model failure of interest are the occurrence of outliers and structural change in the series. An illustration is provided and a simple method of automatically coping with outliers and adapting to change is outlined.