The assessment of monotone dependence between random variables $X$ and $Y$ is a classical problem in statistics and a gamut of application domains. Consequently, researchers have sought measures of association that are invariant under strictly increasing transformations of the margins, with the extant literature being splintered. Rank correlation coefficients, such as Spearman's rho and Kendall's tau, have been studied at great length in the statistical literature, mostly under the assumption that $X$ and $Y$ are continuous. In the case of a dichotomous outcome $Y$, receiver operating characteristic (ROC) analysis and the asymmetric area under the ROC curve (AUC) measure are used to assess monotone dependence of $Y$ on a predictor $X$. In this talk I demonstrate that the two thus far disconnected strands of literature can be unified and bridged, by developing common population level theory, common estimators, and common tests that apply to all types of linearly ordered outcomes. In a case study, we assess recent progress in artificial intelligence based weather prediction (AIWP) versus traditional numerical weather prediction (NWP). The talk is based on joint work with Eva-Maria Walz and Andreas Eberl. This initiative is part of the “Ph.D. Lectures” activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented during the talk.
Geoenergy applications beyond hydrocarbons will play an essential role in accelerating the energy transition: Carbon capture and storage (CCS) is one of the most important approaches to mitigate CO2 emissions; approximately 50% of the energy consumed in the northern hemisphere is needed for heating and cooling, and the expanded use of geothermal energy could lead to significant CO2 reduction; the development of a hydrogen economy for power, transport, and production will rely on intermittent hydrogen storage in geological formations or salt caverns.
All these low-carbon geoenergy applications need bespoke reservoir modelling approaches to estimate available pore volumes for storage, capture how fluids with vastly different properties (e.g. hydrogen vs. hot water) interact with multi-scale geological heterogeneities, and quantify possible operational risks (e.g., early breakthrough of cold water during geothermal energy extraction) while accounting for the uncertainties inherent to geological formations.
This talk will explore how mathematical techniques could be adapted to overcome limitations in existing modelling approaches for low-carbon geoenergy applications. Such new modelling approaches should help to ensure that we design meaningful reservoir models that can provide reservoir performance forecasts with reliable uncertainty bounds, which are needed for new geoenergy applications to advance our transition to a low-carbon energy future.
Contatto:
alessio.fumagalli@polimi.it
