The effect of locational uncertainty in geostatistics
A datum is considered spatial if it contains locational information. Typically, there is also attribute information, whose distribution depends on its location. Thus, error in locational information leads to error in attribute information, which is ultimately reflected in the inference drawn from the data;We propose a statistical model for incorporating locational error into spatial data analysis. We investigate the effect of locational error on the spatial lag, the covariance function, the variogram, and optimal spatial prediction (aka, kriging). We show that the basic methodology of kriging adjusted for locational error is the same as kriging without locational error;We also develop a hierarchical Bayesian model to incorporate locational uncertainty into spatial data analysis. We use Markov chain Monte Carlo techniques to draw from the posterior distribution of the large-scale trend parameters, the covariance-model parameters, the realized site locations, and the process value at a prediction site, given the observed attribute values and the intended sample locations;We use a topographical data set of Davis (1973) as an illustration of kriging without locational error, kriging adjusted for locational error, hierarchical Bayesian kriging without locational error, and hierarchical Bayesian kriging adjusted for locational error. We also investigate, through a simulation study, the effect that varying the trend, the measurement error, the locational error, the range of spatial dependence, the sample size, and the prediction location has on both kriging without locational error and kriging adjusted for locational error.