A Gaussian anamorphosis model for asymmetrically distributed data

Environmental mining and exploration present a challenge for spatial analysis due to small sample sizes and data clustering near mining sites. Additionally, the properties of the covariance function may vary across different mines within the same region, necessitating adaptable geostatistical techniques. A novel approach to analyzing mining data spatial dependence introduces the use of Gaussian Anamorphosis, employing the recently proposed Kernel Cumulative Density (KCDE) method. This technique is particularly effective for data sets that exhibit non-Gaussian distributions, such as the typically asymmetrically distributed natural resources data. Gaussian Anamorphosis through KCDE enables the transformation of skewed probability density functions (PDFs) into the normal distribution. KCDE converts the original data distribution into a continuous cumulative density function (CDF), smoothing out the discontinuities inherent in the traditional staircase CDF estimation approach.
We extend our analysis by conducting Kriging interpolation on the transformed data. Since the transformed data distribution closely approximates the normal distribution, it is possible to use the Kriging variance to reliably estimate prediction intervals before the results are inversely transformed back to their original scale for practical interpretation.
To explore the variability of our results, we implemented Monte Carlo simulations based on the transformed data. The simulations provide insights into the potential outcomes and their variabilities, which were then inversely transformed back to their original scale for practical interpretation.
The findings of this study underscore the effectiveness of Gaussian Anamorphosis using KCDE transformation in dealing with non-Gaussian data distributions in geostatistical analyses. The approach enhances the reliability of spatial predictions and offers robust confidence intervals. Our research demonstrates the potential of combining advanced transformation techniques with geostatistical models to address complex spatial dependencies of natural resources data.

The research project is implemented in the framework of H.F.R.I call “Basic research Financing (Horizontal support of all Sciences)” under the National Recovery and Resilience Plan “Greece 2.0” funded by the European Union – NextGenerationEU (H.F.R.I. Project Number: 16537).