Predicting Exceedance Regions for Geostatistical Processes

• Activity Number: 51
• Type: Invited
• Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Jian Zhang*+ and Noel Cressie and Peter F. Craigmile
• Companies: The Ohio State University and The Ohio State University and The Ohio State University
• Keywords: Baddeley's loss function ; covariance-matching constrained kriging ; integrated weighted quantile squared error loss ; kriging

Abstract

Consider a number of observations drawn from a geostatistical process. It is well known that the optimal linear prediction of linear functionals of the process based on such data is obtained by (universal) kriging of the process. However, kriging is not optimal for nonlinear functions such as extrema of the geostatistical process because kriging oversmoothes the prediction of these functionals by rounding off the peaks and filling in the valleys of the spatial distribution. This oversmoothing leads to incorrect identification of exceedance regions of the geostatistical process. In this poster, we compare methods to improve prediction of exceedance regions. In addition to standard kriging, we evaluate covariance-matching constrained kriging (CMCK) (Aldworth and Cressie 2003) and integrated weighted quantile squared error loss (IWQSEL) prediction (Craigmile et al., 2004). We contrast these plug-in predictions of exceedance regions to a method involving loss functions, where the loss function is distance between sets. These methods are applied to near-surface winds where the goal is to make inference on regions of high winds.