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

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Abstract

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.

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Acknowledgements

We gratefully acknowledge the funding provided by BHP to support this research. We are grateful to the anonymous reviewers for their helpful and constructive comments that greatly helped improve the manuscript.

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Correspondence to Francky Fouedjio.

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Fouedjio, F., Scheidt, C., Yang, L. et al. Conditional simulation of categorical spatial variables using Gibbs sampling of a truncated multivariate normal distribution subject to linear inequality constraints. Stoch Environ Res Risk Assess 35, 457–480 (2021). https://doi.org/10.1007/s00477-020-01925-7

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