Jordan Richards
University of Edinburgh, Scotland
Ciências ULisboa, C6, Floor 4, SASLab – Room 6.2.33
& Teams
22 May 2026 (Friday) – 11h00
Abstract:
Visual and quantitative goodness-of-fit diagnostics are important tools in the practitioner’s toolbox. The need for convincing and reliable diagnostics is particularly clear when fitting extreme value regression models, which are used for extrapolation far beyond the observable range of the response variable and often evaluated at unobserved covariate values. Despite this, few diagnostics have been developed for extreme value regression models, and those available often suffer in terms of interpretability or scalability in the presence of low-dimensional or non-Euclidean covariate domains. Moreover, existing methods tend to offer a global perspective on model fit; that is, they quantify goodness-of-fit across the entire dataset, without offering insight into regions of the covariate space where the model fit may be poor.
We propose two novel visual diagnostics for extreme value regression models: the standardised tail plot and the normalised residual plot. By considering the asymptotic distribution of normalised exceedance probabilities, we show that uncertainty bounds for our plots are approximately independent of the sample size used in their construction. This allows us to propose visual diagnostics which can efficiently and consistently compare goodness-of-fit at both a global and regional level, despite varying sample sizes over regions of the covariate domain. To complement our new visual diagnostics, we propose a new quantitative goodness-of-fit statistic, based on the mean absolute deviation of exponential order statistics, and discuss its theoretical properties. Using two data applications, we showcase how these diagnostics can be used to i) identify regions of covariate space which exhibit poor model fit, ii) facilitate model comparison in the presence of 1000s of candidate models, and iii) help practitioners to improve model design.
Short bio:
Lídia Jordan is based at the University of Edinburgh, Scotland, where he is a Lecturer (equiv. assistant professor) in Statistics and the Director of the Centre for Statistics. Jordan’s research interests include extreme value theory, spatial statistics, statistical machine learning, and Bayesian data analysis. He is a co-organiser for the One World Extremes seminar series, co-creator of the Spatio-Temporal Statistics and Data Science online seminars, and one of the four founders of the Glasgow-Edinburgh Extremes Network, GLE²N.
The CEAUL gratefully acknowledges CEMAPRE for the opportunity to co-sponsor and benefit from Jordan Richards’ visit.
Seminar funded by national funds through FCT – Fundação para a Ciência e a Tecnologia, I.P., under CEAUL Research Unit, UID/00006/2025, DOI: https://doi.org/10.54499/UID/00006/2025, and by the European Union – NextGenerationEU through the project UID/PRR/00006/2025, DOI:https//doi.org/10.54499/UID/PRR/00006/2025.
