Simulating Large Gaussian Random Vectors Subject to Inequality Constraints by Gibbs Sampling

• Published in: Mathematical geosciences Vol. 46; no. 3; pp. 265 - 283
• Main Authors: Emery, Xavier, Arroyo, Daisy, Peláez, María
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2014; Springer Nature B.V
• Subjects: Algorithms; Annealing; Chemistry and Earth Sciences; Computer Science; Computer simulation; Conditioning; Earth and Environmental Science; Earth Sciences; Gaussian; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Inequalities; Iterative algorithms; Markov analysis; Mathematical analysis; Mathematical models; Mining engineering; Physics; Statistics for Engineering; Vectors (mathematics); Markov chain; Gibbs sampler; Gaussian random field; Kriging neighborhood; Restriction of transition matrix; Simulated annealing
• ISSN: 1874-8961; 1874-8953
• DOI: 10.1007/s11004-013-9495-9

The Gibbs sampler is an iterative algorithm used to simulate Gaussian random vectors subject to inequality constraints. This algorithm relies on the fact that the distribution of a vector component conditioned by the other components is Gaussian, the mean and variance of which are obtained by solving a kriging system. If the number of components is large, kriging is usually applied with a moving search neighborhood, but this practice can make the simulated vector not reproduce the target correlation matrix. To avoid these problems, variations of the Gibbs sampler are presented. The conditioning to inequality constraints on the vector components can be achieved by simulated annealing or by restricting the transition matrix of the iterative algorithm. Numerical experiments indicate that both approaches provide realizations that reproduce the correlation matrix of the Gaussian random vector, but some conditioning constraints may not be satisfied when using simulated annealing. On the contrary, the restriction of the transition matrix manages to satisfy all the constraints, although at the cost of a large number of iterations.