1. If no transformation is applied, the underlying model is an intrinsic random function, specifically a Power semivariogram model. If a transformation is applied, it is a simple kriging model with an exponential semivariogram.
2. The prior distribution is estimated from the data using restricted maximum likelihood (REML). This is the difference between "Bayesian" and "empirical Bayesian." In empirical Bayesian models, the prior is estimated from the data, and the posterior distribution is generated through simulations.
3. There are several reasons to think EBK will, in general, be more accurate. First, REML is known to be a better estimator of semivariogram parameters than weighted least-squares (which is what is used in other kriging methods). Second, EBK works on subsets, so it eases the stationarity assumption of kriging. Other kriging methods assume global stationarity. EBK, however, only assumes stationarity within subsets, so it can work effectively even in the presence of global nonstationarity, as long as the subsets are close to being stationary. Third, EBK does a better job of estimating kriging variances because it can account for error in estimating the underlying semivariogram (it does this with simulations); other kriging models assume the semivariogram is modeled absolutely correctly, which often results in standard errors that are too small.
Here is a reference for EBK (a longer paper with all the details is in the works):
Krivoruchko K. and Gribov A. (2014) Pragmatic Bayesian kriging for non-stationary and moderately non-Gaussian data. Submitted. In Mathematics of Planet Earth. Proceedings of the 15th Annual Conference of the International Association for Mathematical Geosciences. Eds: Pardo-Igúzquiza, E.; Guardiola-Albert, C.; Heredia, J.; Moreno-Merino, L.; Durán, J.J.; Vargas-Guzmán, J.A. Springer 2014, pp. 61-64.
(We're not sure why the date is 2014 because it's already been published)
