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Mathematical Sciences Colloquium and Statistics Seminar by Ryan Martin (NCSU)
Friday, April 14, 2023 3pm to 4pm
Science Learning Center (SLC), 1.102
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Event Details
A possibility-theoretic solution to the Bayesian-versus-frequentist predicament.
There are two mainstream schools of thought in statistics: Bayesian and frequentist. While the public debates between the two camps have subsided, the underlying foundational questions remain unanswered -- and the embarrassment and confusion associated with having two accepted but fundamentally different theories persists. Previous attempts have been made to close this gap, most notably Fisher's fiducial argument, but the consensus is that these attempts have failed. What these failed attempts have in common is that they propose to quantify uncertainty about the unknown in terms of a data-dependent probability distribution. In this talk, I'll argue that the likelihood (model + data) alone can't reliably support this kind of probabilistic inference. Therefore, in order to settle this predicament, it's necessary to consider more general uncertainty theories. Following some background, I'll present my proposed solution that's rooted in *possibility theory*. I'll highlight what is familiar and unfamiliar about my proposed solution, what key properties it satisfies, and show some examples. For most of the presentation, I'll focus on the case where there's a complete lack of genuine prior information about the unknown. Time permitting, I'll talk about how to push this imprecise-probabilistic perspective to its limit by allowing for the incorporation of partial/incomplete prior knowledge.
Location
Science Learning Center (SLC), 1.102
800 W. Campbell Road, Richardson, Texas 75080-3021
Department
- Natural Sciences & Mathematics
Contact Information
- Chuan-Fa Tang
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