Assessing the spatial heterogeneity of environmental variables is a challenging problem in real applications when numerical approaches are needed. This is made more difficult by the complexity of Natural Phenomena, which are characterized by (Chiles and Delfiner, 2012):
- being unknown: their knowledge is often incomplete, derived from limited and sparse samples;
- dimensionality: they can be represented in two- or three-dimensional domains;
- complexity: deterministic interpolators (i.e., Inverse Distance Weighted) may fail in providing exhaustive spatial distribution models, as they do not consider uncertainty;
- uniqueness: invoking a probabilistic approach, they can be assumed as a realization of a random process and described by regionalized variables.
Geostatistics provides optimal solutions to this issue, offering tools to accurately predict values and uncertainty in unknown locations while accounting for the spatial correlation of samples.

The course will address theoretical and practical methods for evaluating data heterogeneity in computational domains, exploiting the interplay between geometry processing, geostatistics, and stochastic approaches. It will be mainly split into 4 parts, as follows:
- Theoretical Overview: Introduction to Random Function Theory and Measures of Spatial Variability
- Modeling Spatial Dependence: An automatic solution to detect both isotropic and anisotropic spatial correlation structures
- The role of Unstructured Meshes: Exploration of flexible, robust, and adaptive geometric modeling, coupled with stochastic simulation algorithms
- Filling the Mesh: Developing a compact and tangible spatial model, that incorporates all alternative realizations, statistics, and uncertainty

The course will offer a comprehensive understanding of key steps to create a spatial predictive model with geostatistics. We will also promote MUSE (Modeling Uncertainty as a Support for Environments) (Miola et al., STAG2022) as an innovative and user-friendly open-source software, that implements the entire methodology. Tips on how to use MUSE will be provided, along with explanations of its structure and executable commands. Impactful examples will be used to show the effectiveness of geostatistical modeling with MUSE and the flexibility to use it in different scenarios, varying from geology to geochemistry.

The course is designed for everyone interested in geostatistics and spatial distribution models, regardless of their prior experience.