Gibbs Sampler

Abstract

Our ultimate objective is to simulate a gaussian random function with a specified covariance structure, given the observed lithotypes (facies) at sample points. As the lithotypes are known at these points, the corresponding gaussian variables must lie in certain intervals but their values are not known. So we need to simulate a gaussian random function subject to interval constraints. A two step procedure is used to do this. Firstly a Gibbs sampler is used to generate gaussian values at sample points that have the right covariance and belong to the right intervals. Once we have this set of point values, any method for conditionally simulating gaussian random functions can be used; for example, turning bands together with a conditioning kriging, sequential gaussian simulations, LU decomposition, etc. See Chiles and Delfmer (1999), Lantuéjoul (2002) or Deutch and Journel (1992). As these techniques are well known, we will not dwell on them here.