A new MOX Report entitled “Estimating Non-Stationarity in Spatial Processes: an approach based on Random Domain Decomposition” by Scimone, R.; Menafoglio, A.; Secchi, P. has appeared in the MOX Report Collection.
Check it out here: https://www.mate.polimi.it/biblioteca/add/qmox/13-2025.pdf
Abstract: The present work addresses the problem of flexible and efficient parameter estimation for non-stationary Gaussian random fields. This problem is crucial to enable modeling and stochastic simulation of complex natural phenomena in the Earth Sciences. Building on the non-stationary Matérn model of Paciorek and Schervish (2006), we propose a novel computational method that leverages random and repeated domain partitions to construct locally stationary estimates. Unlike existing approaches that rely on fixed grids of knots, our method employs a bagging-type strategy to mitigate the influence of domain decompositions in a divide-and-conquer fashion. This results in more robust and adaptive estimations, overcoming key limitations of traditional methods. Through extensive simulations and a real case study, we demonstrate that while fixed grids noticeably impact the final estimated models, our approach produces grid-free estimations, thanks to ! the addit ional source of randomness introduced by the aleatory partitions of the domain.
