Analyzing censored spatial data

Spatial data that are incomplete because of observations arising below or a bove a detection limit occur in many settings, for example, in mining, hydr ology and pollution monitoring. These observations are referred to as censo red observations. For example, in a life test, censoring may occur at rando m times because of accident or breakdown of equipment. Also, censoring may occur when failures are discovered only at periodic inspections. Because th e informational content of censored observations is less than that of uncen sored ones, censored data create difficulties in an analysis, particularly when such data are spatially dependent. Traditional methodology applicable for uncensored data needs to be adapted to deal with censorship. In this pa per we propose an adaptation of the traditional methodology using the so-ca lled Expectation-Maximization (EM) algorithm. This approach permits estimat ion of the drift coefficients of a spatial linear model when censoring is p resent. As a by-product, predictions of unobservable values of the response variable are possible. Some aspects of the spatial structure of the data r elated to the implicit correlation also are discussed. We illustrate the re sults with an example on uranium concentrations at various depths.