A loss function approach to identifying environmental exceedances
This article deals with the loss function approach to identifying environmental exceedances. The authors introduce the hierarchical spatial model and define the averaged cumulative distribution function and the integrated weighted quantile squared error loss function. There are presented several intuitively useful examples of integrated weighted quantile squared error loss functions for weight functions that can be used for estimating extrema and the authors calculate the optimal Bayes predictor relative to an arbitrary integrated weighted quantile squared error loss function. A hierarchical spatial model for pollutant concentrations based on the lognormal distribution is considered. Bayesian posterior inference derived from the model is discussed. An illustrating example shows how the methodology can be applied to the problem of estimating exceedances of surface-nitrogen concentrations in the Chesapeake Bay.
integrated weighted quantile squared error loss
scientific article; zbMATH DE number 5158673
scientific article