Variogram is simple but effective way to investigated the spatial variation in the variable of interest in the field being studied. However it has been reported that variogram cannot be considered as the most satisfactory model especially where there are curvature (e.g., permeable channels in reservoir engineering) in the medium being studied. That is different patterns could have more and less exact copy of the same variogram.
A suggestion for development an approach was multi-point statistics (geostatistics), in which for example, a training image, a 2D matrix template is being used for inference of spatial variation. It was shown in the literature that training images are useful to dictate the output the desired pattern honoring conditioning data and being based on stochastic approaches to satisfy statistical inferences.
Q1: What else about advantages and or disadvantages of multi-point statistics ?
Q2: How to obtain training images?
__Q2.1: How to generate training images using existing knowledge etc?
Q3: How about 3D and further dimensions?
Q3: What is the next stage after training image?