Conditional simulation of categorical spatial variables using Gibbs sampling of a truncated multivariate normal distribution subject to linear inequality constraints

• Published in: Stochastic environmental research and risk assessment Vol. 35; no. 2; pp. 457 - 480
• Main Authors: Fouedjio, Francky, Scheidt, Celine, Yang, Liang, Wang, Yizheng, Caers, Jef
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2021; Springer Nature B.V
• Subjects: Aquatic Pollution; Chemistry and Earth Sciences; Computational Intelligence; Computer Science; Conditioning; Earth and Environmental Science; Earth Sciences; Environment; Linear functions; Math. Appl. in Environmental Science; Normal distribution; Original Paper; Physics; Principal components analysis; Probability Theory and Stochastic Processes; Sampling; Simulation; Statistics for Engineering; Waste Water Technology; Water Management; Water Pollution Control; Gibbs sampler; Conditional simulation; Categorical spatial variable; Implicit function; Principal component analysis
• ISSN: 1436-3240; 1436-3259
• DOI: 10.1007/s00477-020-01925-7

This paper introduces a method to generate conditional categorical simulations, given an ensemble of partially conditioned (or unconditional) categorical simulations derived from any simulation process. The proposed conditioning method relies on implicit functions (signed distance functions) for representing the categorical spatial variable of interest. Thus, the conditioning problem is reformulated in terms of signed distance functions. The proposed approach combines aspects of principal component analysis and Gibbs sampling to achieve the conditioning of the unconditional categorical realizations to the data. It is applied to synthetic and real-world datasets and compared to the traditional sequential indicator simulation. It appears that the proposed simulation technique is an effective method to generate conditional categorical simulations from a set of unconditional categorical simulations.