Statistics Seminar by Jose Miguel Angulo, the University of Granada, Spain

Abstract:

Spatial deformation has been considered, among other purposes, to account for heterogeneities present in the dependence structure or the dynamics of spatiotemporal random fields, that can be linked to the physical support space.

In relation to characterization of extremal behaviour of random field realizations, and subsequently for risk assessment, the geometrical-probabilistic analysis of excursion sets defined by threshold exceedances has motivated a vast theoretical and methodological research literature.

These are two prominent examples of space (or space-time) and state transformations that can be, conceptually and formally, interpreted as extended or restricted random field model formulations.

In this seminar, we review and discuss some aspects and approaches contributed withinthis framework, including the combination of both space and state transformations, information-theoretic analysis, as well as ongoing and potential developments under aninfinite-dimensional perspective. Particularly, we are motivated by the geometrical analysis of functional Neural Network Gaussian Fields (fNNGFs) in the context of infinite-width analysis of random neural networks.