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Botzmann-Gibbs distributions beyond statistical physics: Gaussian processes, spatiotemporal statistics and machine learning. Presented at the 48th Meeting of the Middle European Cooperation in Statistical Physics, Stara-Lesna, Slovakia, May 24, 2023.

During this talk I will present a personal perspective on current topics of research in Geostatistics. As a result of the ongoing data revolution, large amounts of spatial and spatiotemporal data are often available for analysis.  Traditional geostatistical methods, however, have been developed before the era of data explosion, and they are not designed to handle well big data volumes, spatiotemporal data, or data of diverse types. Hence, there is a need for flexible and computationally efficient methods for spatial and --- even more so --- for spatiotemporal data analysis. In addition to mining engineering, a number of scientific and engineering disciplines (e.g., applied mathematics, mechanical engineering, and computer science) are facing similar problems of data analysis and data fusion with first-principles mathematical models. I strongly believe that progress towards the solution of the methodological problems can be accelerated by closer inter-disciplinary collaboration.  

The particular approach that I will discuss for the modeling and analysis of large datasets is based on the simple idea of locality, i.e.., the fact that spatial and spatiotemporal correlations can be modeled by means of local interactions between neighboring data values. The idea of locality is embodied in the statistical field theories of physics and in the theory of Gauss Markov random fields. After a short introduction to classical Geostatistics, I will discuss the local approach to Geostatistics that I have been developing in collaboration with graduate students and postdoctoral researchers.  This approach utilizes concepts from statistical physics and machine learning.  Several interesting and practical results have been obtained in this framework, including novel spatial and spatiotemporal covariance functions, as well as computationally efficient methods of spatial estimation and extensions of Gauss-Markov random fields to data that are scattered in space. I will illustrate some of the salient properties of the new local framework using data from mining and environmental case studies.  I will conclude the presentation by suggesting future directions of research and by identifying specific applications of potential interest to mining engineering.  

Invited Presentation, Workshop on Stochastic models for climate-related risk, organized by the
Lebesgue Center of Mathematics at the University of Bretagne Sud, France.
Title: “Stochastic Local Interaction Models and Space-Time Covariance Functions based on
Linear Response Theory”

Organized with Tetsu Uesaka (Mid-Sweden University) the mini-symposium "MS 1305:
Stochastic Models of Failure In Random Heterogeneous Materials And Complex Networks" at the 7th European Congress on Computational Methods in Applied Sciences and Engineering, Hersonisos, Crete, Greece: June 2016.