Probability Seminar: Vianey Palacios Ramirez - Heavy Tails and Random Measures: New Perspectives via Two Constructions: Subordinators and Stick-Breaking
| Dates: | 19 November 2025 |
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| Times: | 15:00 - 16:30 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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Vianey Palacios Ramirez (Newcastle University) will speak at the Probability seminar.
Title:
Heavy Tails and Random Measures: New Perspectives via Two Constructions: Subordinators and Stick-Breaking
Abstract:
Modeling heavy tails is essential in the study of extreme events, where the probability of rare but impactful outcomes must be accurately captured. In Bayesian nonparametrics, random probability measures (RPMs) are widely used, and understanding their tail behavior is key when applying them to extremes. This talk explores the tail behavior of RPMs through two foundational constructions: normalization of subordinators and stick-breaking representations. In the case of subordinators, tail properties can be studied via the Lévy measure, providing a direct link between the tail of the RPM and that of the underlying stochastic process. However, for more general stick-breaking constructions, such a direct connection is often unavailable. To address this, we introduce a framework based on transport between measures: by constructing a measurable map from a RPM with known tail behavior to one with unknown tails, we can transfer tail properties and derive new results. Each construction requires a distinct analytical perspective, and the transport approach offers a flexible tool that can be generalized to study a wider class of models.
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Frank Adams 2
Alan Turing Building
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