Statistics and Risk Management Seminar (double session)

Department of Mathematics, NOVA MATH/FCT NOVA

Seminar I

Title: Induced nonparametric ROC surface regression

Speaker: Vanda Inácio; University of Edinburgh, Scotland

Date | Time: July 14, 2026 | 14:00

Location: Hangar II, room 2

Teams: https://teams.microsoft.com/meet/36124291051668?p=9wzuxJVsdpJQkGb9ww

Abstract: The receiver operating characteristic (ROC) surface is a popular tool for evaluating the discriminatory ability of diagnostic tests measured on a continuous scale when there exist three ordered disease groups. Motivated by the impact that covariates may have on the diagnostic accuracy, and to safeguard against model misspecification, we develop a flexible model for conducting inference about the covariate-specific ROC surface and its functionals. Specifically, we postulate a location-scale regression model for the test outcomes in each of the three disease groups where the mean and variance functions are estimated through penalised-splines, while the distribution of the error term is estimated via a smoothed version of the empirical cumulative distribution function of the standardised residuals. Our simulation study shows that our approach successfully recovers the true covariate-specific volume under the surface and optimal pair of thresholds in a variety of scenarios. Our methods are motivated by and applied to data derived from an Alzheimer's disease study and we seek to assess the accuracy of several  biomarkers to distinguish between individuals with normal cognition, mild cognitive impairment, and dementia and how this discriminatory ability may change with the age and gender.

Seminar II

Title: Extremal Vulnerability

Speaker: Miguel de Carvalho; University of Edinburgh & University of Aveiro

Date | Time: July 14, 2026 | 15:30

Location: Hangar II, room 2

Teams: https://teams.microsoft.com/meet/36124291051668?p=9wzuxJVsdpJQkGb9ww

Abstract: In many complex systems, identifying the most vulnerable component is essential for effective prevention, intervention, and risk management. In this talk, I will introduce the notion of extremal vulnerability, defined as the long run tendency of a component to be affected by extreme events occurring in other components. The proposed framework builds on the tail dependence matrix and introduces the Extremal Vulnerability Rank (XVRank) method—a PageRank-inspired algorithm designed to quantify extremal vulnerability.  We establish the theoretical properties of the proposed inferences, including consistency and asymptotic normality, and validate their performance through Monte Carlo simulations. The proposed methods are illustrated using financial data to determine assets most exposed to severe market downturns. Joint work with P. Redondo, R. Huser, and H. Ombao (KAUST).

Organizers: Isabel Natário and Mina Norouzirad and Miguel Fonseca

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This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UID/00297/2025 (\url{https://doi.org/10.54499/UID/00297/2025}) and UID/PRR/00297/2025 (\url{https://doi.org/10.54499/UID/PRR/00297/2025}) (Center for Mathematics and Applications)

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