Once the ordinary kriging model has been applied, these estimates can be used to update the initial estimate of the prior distribution to the posterior distribution at each node on the grid. Johnson (1996) used a heuristic approach to estimate the amount of information from the correlated sample results to insert into the Bayesian update equations based on independent results. His proposal is that the parameters of the Beta distribution be updated using x* = n* p(z0) with .

is the nugget and c is the sill of an assumed exponential semivariogram model (see Spatial Correlation), F2(z0) is the ordinary kriging variance at Z0, and p(z0) is the standard ordinary kriging estimation of the probability of exceeding the threshold at z0. Here, n* is the number of pseudo samples. Using the values for X* and n*, you can update the values of : and Fat Zo with the following formulas.

and