University of Washington - Department of Statistics
We consider the problem of calibrated and sharp probabilistic forecasting of a future meteorological quantity. By calibrated, we mean that if we define a predictive interval, such as a 90% probability interval, then on average in the long run, 90% of such intervals contain the true value. By "sharp," we mean that the distribution is more concentrated than forecast distributions from climatology (i.e. the marginal distribution) alone. UW Atmospheric Science Professor Cliff Mass and his group have developed an ensemble forecasting system for the Pacific Northwest based on a set of weather forecasting deterministic simulation models. He has established a clear relationship between between-model variability and forecast errors, but his forecast intervals are generally not calibrated; they are too narrow. This seems contradictory at first sight. We apply Bayesian model averaging to develop probability forecasts using Mass's ensemble. The theory of Bayesian model averaging explains both of Mass's main empirical findings: the spread-error relationship, and the fact that the intervals from the Mass ensemble are too narrow on average. We develop Bayesian model averaging forecasts and apply them to forecasts of sea-level pressure in the Pacific Northwest. The resulting forecasts are calibrated and sharp. This is joint work with Fadoua Balabdaoui, Tilmann Gneiting and Michael Polakowski, and was supported by the DOD MURI Program.