@Christian Ungewitter

Mr. Merks is not so wrong. Loopholes are everywhere. But, many geoscientists are statistically very strong. So, it is very difficult to conclude that geoscientists are theoretically fraud or sound.

Dear Mr. Massimiliano Alvioli ,

thank you for your reply. It is true that geostatistics, like statistics in general, are often used and abused. But do you think that there are major flaws in the theoretical foundations of geostatistics besides the apllication by the users?

Jan Merks is one of the best statisticians I have ever come across and I follow most of his work. However, I tend to differ on labelling the entire geostatistics discipline as ’voodoo or scientific fraud’.

Like any other discipline in science and engineering, geostatistics has its positives and negatives. To call it a scientific fraud is a little bit subjective. The discipline has evolved since its initial development. I still have my concerns on the multitude of steps that one needs to go through before kriging. The pre-kriging steps are all based on classic statistics principles, hence minimising some errors on the assumption of stationarity and Homoscedasticity. The theory of the discipline is based on sound statistics and much of what has been criticised now forms part of the estimation process e.g., degrees of freedom and variance of each estimate. We calculate appropriate min and max samples before running the estimates. It's important to note that inexperienced practitioners are likely to only split the data into geodomains and krig without following the pre-treatment steps that need to be considered before kriging. Such users or practitioners are the ones that bring animosity to the discipline.

I have also noticed the many users do not fully understand the mathematics and statistics behind the kriging equations and heavily rely on commercial software. While this can be a cost-saving initiative for corporations, it often leads to bad estimates and creates room for the critics to lay blame on the discipline rather than the user.

It would certainly also be helpful to supplement some of the excellent previous answers and to extend the discussion to other areas of spatial statistics beyond geostatistics. There are, for example, exploratory spatial data analysis, spatial econometrics, and point pattern analysis. All of these areas have been the subject of intensive and interdisciplinary research for decades. Treatises at different levels of technical sophistication have emerged in the process. In my opinion, however, it is precisely this diversity of thought and consideration from different angles that has led to solid theoretical foundations in each case. These fields also share many basic concepts (such as spatial autocorrelation), which has led to their redundant consideration of different communities. The latter could also be seen as a kind of cross-evaluation of concepts, which ensures the validity of corresponding methods. What is certainly true, as already mentioned, is that some users do not apply spatial statistical methods adequately. However, this problem also exists in non-spatial statistics, although in the spatial domain the problem may be greater due to several necessary conceptualisation steps, each requiring both technical and domain knowledge.