A model-based geostatistical approach for skewed radioactivity data

In the last years, to improve the performance of prediction of radioactive contamination, an increasing number of studies have explored and exploited the potentials of geostatistical methods. However, traditional methods like kriging and cokriging are optimal only in the case in which the data may be assumed Gaussian and do not properly cope with data measurements that are discrete, nonnegative or show some degree of skewness, as in many environmental applications concerned with radioactivity measurements. To deal with geostatistical skewed data, we consider a model-based approach in which measurements are modeled with the help of a latent Gaussian structure and some recent classes of skewed distributions extending the normal one. For our model we investigate the implied spatial autocorrelation structure and the marginal distributions of the observable variables. In particular we show that all finite-dimensional marginal distributions of the observable variables belong to the family of the unified skew-normal distribution. Estimation of some of the unknown parameters of the model can be carried out by employing a Monte Carlo expectation maximization procedure, whereas predictions of both latent and observed (at unsampled sites) variables, can be supplied by Markov chain Monte Carlo algorithms.