Analyzing Censored Spatial Data

Abstract

Spatial data that are incomplete because of observations arising below or above a detection limit occur in many settings, for example, in mining, hydrology, and pollution monitoring. These observations are referred to as censored observations. For example, in a life test, censoring may occur at random times because of accident or breakdown of equipment. Also, censoring may occur when failures are discovered only at periodic inspections. Because the informational content of censored observations is less than that of uncensored 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 paper we propose an adaptation of the traditional methodology using the so-called Expectation-Maximization (EM) algorithm. This approach permits estimation of the drift coefficients of a spatial linear model when censoring is present. As a by-product, predictions of unobservable values of the response variable are possible. Some aspects of the spatial structure of the data related to the implicit correlation also are discussed. We illustrate the results with an example on uranium concentrations at various depths.