The multiGaussian approach provides a parametric approach to infer the conditional distribution at unsampled locations. An alternative to that model is given by the indicator framework. In the indicator framework, the original variable is converted into a vector of indicators and each new variable (each indicator) is characterized and modeled separately.
For continuous variables, the indicators represent the probability of not exceeding a threshold. Therefore, they discretize the cdf. Once each indicator has been estimated by kriging, after inferring and modeling its 3D variogram, the kriged indicators can be interpreted as an estimate of the probability of not exceeding the corresponding threshold, and an “estimated cdf” can be constructed.
This local cdf provides information about the local uncertainty of the variable. The approach can be adapted to categorical variables as well. A vector of indicator variables can replace the categorical value at every location.
Each indicator represents the probability of a specific category prevailing at that location. Assuming the categories are exhaustive and mutually exclusive, then the indicator represents the probability of finding a specific category at each location.
Again, we can characterize these categorical indicators by computing and modeling their 3D variogram. Then kriging can be performed to estimate the probability of each category prevailing at unsampled locations.
These categories must sum to one (this is imposed as a post-processing correction). Then a single category can be selected from the local cumulative mass function. Although more flexible than the multiGaussian approach, the indicator framework is much more laborious, and often brings practical challenges.
Download: 09-Geostatistics Uncertainty Indicators
Credits to Julián M. Ortiz
