Generating Probabilities From Numerical Weather Forecasts by Logistic Regression

Abstract

Logistic models are studied as a tool to convert output from numerical weather forecasting systems (deterministic and ensemble) into probability forecasts for binary events. A logistic model obtains by putting the logarithmic odds ratio equal to a linear combination of the inputs. As any statistical model, logistic models will suffer from over-fitting if the number of inputs is comparable to the number of forecast instances. Computational approaches to avoid over-fitting by regularisation are discussed, and efficient approaches for model assessment and selection are presented. A logit version of the so called lasso, which is originally a linear tool, is discussed. In lasso models, less important inputs are identified and discarded, thereby providing an efficient and automatic model reduction procedure. For this reason, lasso models are particularly appealing for diagnostic purposes.