Adrian E. Raftery

University of Washington


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 alone. Mass has developed an ensemble
mesoscale forecasting system 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. 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 and Bayesian Model Averaging
forecasts and apply them to Puget Sound winter temperatures. The resulting
forecasts are well calibrated and sharp.

This is joint work with Tilmann Gneiting, Fadoua Balabdaoui and Michael
Polakowski. It was supported by the DOD MURI Program.