Topological obstacles to shared priors

Abstract: Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on the full space? This formulation of the consistency problem for conditional probabilities is significant in Bayesian epistemology and probabilistic reasoning, as it describes the conditions under which a collection of agents can reach agreement by sharing information. We derive a necessary and sufficient condition under which joint compatibility is equivalent to pairwise compatibility. This condition is stated in terms of the cohomology of a simplicial complex constructed from the given probability measures, exposing a novel application of algebraic topology to Bayesian reasoning.

Speaker Bio: Michael G. Titelbaum is a Vilas Distinguished Achievement Professor in the Department of Philosophy at the University of Wisconsin-Madison. He has published Quitting Certainties and Fundamentals of Bayesian Epistemology, both with Oxford University Press. He received a PhD in Philosophy from the University of California, Berkeley in 2008. Before doing that, he was a high school math teacher for four years.

Moderator: Ted Theodosopoulos. Ted is a mathematician who, after working for years in academia and industry, transitioned to teaching at the pre-college level sixteen years ago, the last eight at Nueva, where he teaches math and economics. Ted’s research background is in the area of interacting stochastic systems, with particular applications in biology and economics.

Computer scienceMathematics

Audience: researchers in the topic

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Relatorium seminar

Series comments: The name "Relatorium" combines "relator" with the Latin root "-ium," meaning "a place for activities" (as in "auditorium" or "gymnasium"). This seminar series is a platform to relate ideas, interact with math, and connect with each other.

In this series, we explore math beyond what we usually hear in standard talks. These sessions fall somewhere between a technical talk and a podcast: moderately formal, yet conversational. The philosophy behind the series is that math is best learned by active participation rather than passive listening. Our aim is to “engage and involve,” inviting everyone to think actively with the speaker. The concepts are accessible, exploratory, and intended to spark questions and discussions.

The idea of relatability has strong ties to compassion — creating space for shared understanding and exploration - which is the spirit of this seminar! This is a pilot project, so we’re here to improvise, learn, and evolve as we go!

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