Conditioning a Gaussian model with inequalities

Abstract

Functions with mixed discrete/continuous distribution, random sets or coregionalizations between a function and a random set can be modelled using gaussian random functions. In these cases, the conditions at experimental points are expressed in terms of inequalities: 1 ≤ i ≤ n, a i ≤ X i ≤ b i . The simulation with composite constraints (equalities and inequalities) is performed in two steps: firstly we ensure that the inequality constraints are validated, secondly we perform a classic conditional simulation. To validate the inequalities, we propose two methods: the first one is based on the acceptance-rejection technique but can be used only to validate very few inequalities; in the second, we sample the stationary distribution of a Markov chain. This latter case is illustrated with a few examples.