Spatial prediction with left-censored observations

Environmental monitoring of contaminants often involves left-censored observations falling below the minimum detection limits (MDLs) of the instruments used to assay their concentrations. Statistical procedures for handling left-censored observations generally assume that the observations are independently distributed. However, data collected over a spatial network of sample sites are likely to be spatially correlated. This correlation structure can be exploited to obtain improved imputations of left-censored observations, and hence improved estimates of environmental parameters. This article applies a Robbins-Monro algorithm for estimating the parameters of a spatial regression model. This algorithm uses importance sampling to obtain conditional simulations of left-censored observations. A predictor for data at unsampled sites is obtained by taking the weighted mean of kriging predictors computed from independent importance samples. The proposed methods are illustrated using data from the South Florida Ecosystem Assessment Project.