Causal inference in the tails: extreme event attribution, treatment effects, and structural discovery

Li, Mengran (2026) Causal inference in the tails: extreme event attribution, treatment effects, and structural discovery. PhD thesis, University of Glasgow.

Abstract

Many consequential questions about rare, high-impact events, including heatwaves, financial crashes, severe adverse drug responses, and extreme precipitation, arise in the tail of the distribution. These events are difficult to analyse because observations are scarce, methods designed for typical outcomes can be unreliable in the regions of interest, and the questions being asked often concern interventions, counterfactuals, or structural propagation rather than descriptive probabilities alone. Extreme value theory provides principled tools for modelling tail behaviour, while causal inference provides a language for interventions and counterfactual reasoning. Yet standard causal assumptions about support, overlap, and stability are often most fragile in the tail. This thesis develops a coherent methodological perspective on causal inference for extremes through the connected tasks of attribution, estimation, and discovery.

The first contribution addresses attribution through a sensitivity framework within a counterfactual setting, examining how attribution metrics vary across alternative marginal and joint-tail specifications. In the simulations and two precipitation applications, estimates vary materially across the three fitted tail models, in some cases changing sign. The results show that attribution conclusions can be sensitive to both marginal and dependence modelling choices. The second contribution focuses on estimation via the Tail-Calibrated Inverse Estimating Equation (TIEE) for extreme quantile treatment effects. TIEE combines causal adjustment with tail calibration, allowing information from less extreme quantiles to stabilise inference at extreme levels where direct quantile estimation is unreliable. By embedding extreme value structure within a unified estimating equation, TIEE enables rigorous causal attribution for outcomes so rare that standard methods become ineffective. The third contribution addresses discovery through Sparse Structure diScovery in Multivariate Extremes (S3ME), a two-stage method for learning sparse extremal causal structure. By combining skeleton estimation with edge orientation based on tail-induced asymmetry, S3ME recovers propagation pathways in settings characterised by heavy tails and latent shocks, with applications to hydrological and financial tail-risk systems.

Across these three components, the thesis shows that causal inference in the tails cannot be treated as a straightforward extension of standard methods. Tail assumptions fundamentally shape the estimands, the stability of inference, and the recoverable structures. As such, extreme value modelling and causal reasoning must be developed jointly, rather than applied as separate sequential tools.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics
• Supervisor's Name: Castro-Camilo, Dr. Daniela
• Date of Award: 2026
• Depositing User: Theses Team
• Unique ID: glathesis:2026-86210
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 08 Sep 2026 14:50
• Last Modified: 08 Sep 2026 15:06
• Thesis DOI: 10.5525/gla.thesis.86210
• URI: https://theses.gla.ac.uk/id/eprint/86210

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