Mike Titelbaum and Ted Theodosopoulos - Topological Obstacles to Shared Priors

From the video description:

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.

See Topological Obstructions to Shared Priors by Owen D. Biesel, Colin McSwiggen, Ted Theodosopoulo and Michael G. Titelbaum. 

See also Aumann's Agreement Theorem is Fifty Years Old.

Subscribe to Relatorium. 

I had a strange dream this morning. I had learned some weird language invented at Bell Labs which was all about decomposing complicated things according to some sort of bases and there was some sort of notion of octave involved. The kinds of construction involved large matrix-like things with complex symmetries. I was very pleased with myself for having understood enough of this language to do whatever I had done, and then someone told me that the only problem at Bell Labs was that there were these two groups of Indians who never spoke to each other. They were very nice, she said, but just that in India they didn't speak to each other, and those that worked at Bell Labs maintained the tradition. Then I woke up. 

It must've been something to do with calculating surgery on topological spaces of Bayesian priors. 



Subscribe to Daniel Tubbenhauer. 

See Terence Tao Formalising Riemann-Stieltjes Integrals in Lean Mathlib. 

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