Bayesian Inference and Prediction of Gaussian Random Fields Based on Censored Data

Victor De Oliveira
University of Arkansas



This work develops a Bayesian approach to perform inference and prediction
in Gaussian random fields based on spatial censored data. This type of data
occurs often in the earth sciences due either to limitations of the measuring
device or particular features of the sampling process used to collect the data.

Inference and prediction on the underlying Gaussian random field is
performed, through data augmentation, by using Markov chain Monte Carlo
methods. Previous approaches to deal with spatial censored data are reviewed,
and their limitations pointed out.

The proposed Bayesian approach is applied to a spatial dataset of depths
of a geologic horizon that contains both left and right censored data, and
comparisons are made between inferences based on the censored data and
inferences based on `complete data' obtained by two imputation methods.
It is seen that the differences in inference between the two approaches
can be substantial.