# Multiple imputation framework for data assignment in truncated pluri-Gaussian simulation

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## Abstract

Truncated pluri-Gaussian simulation (TPGS) is suitable for the simulation of categorical variables that show natural ordering as the TPGS technique can consider transition probabilities. The TPGS assumes that categorical variables are the result of the truncation of underlying latent variables. In practice, only the categorical variables are observed. This translates the practical application of TPGS into a missing data problem in which all latent variables are missing. Latent variables are required at data locations in order to condition categorical realizations to observed categorical data. The imputation of missing latent variables at data locations is often achieved by either assigning constant values or spatially simulating latent variables subject to categorical observations. Realizations of latent variables can be used to condition all model realizations. Using a single realization or a constant value to condition all realizations is the same as assuming that latent variables are known at the data locations and this assumption affects uncertainty near data locations. The techniques for imputation of latent variables in TPGS framework are investigated in this article and their impact on uncertainty of simulated categorical models and possible effects on factors affecting decision making are explored. It is shown that the use of single realization of latent variables leads to underestimation of uncertainty and overestimation of measured resources while the use constant values for latent variables may lead to considerable over or underestimation of measured resources. The results highlight the importance of multiple data imputation in the context of TPGS.

## Keywords

Geostatistics Geomodeling Missing data analysis Gibbs sampler## References

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