Evaluating Predictive Performance
Many statistical methods such as (generalized) linear regression, time series approaches or geostatistical techniques are concerned with forecasting and interpolating uncertain, unknown, or partially known quantities. To address and quantify prediction uncertainty, the forecaster ought to provide a full predictive probability distribution over the quantity or event of interest, rather than just a point forecast. In this paper we provide a brief review on diagnostic and quantitative methods for the evaluation of predictive distributions that have developed in the context of probabilistic forecasting. We also discuss the issue of deriving optimal point forecasts from a predictive distribution and illustrate the proposed evaluation methods with a data example on one day ahead predictions of ozone concentrations.
KeywordsEigenvalue method Model reduction Groundwater