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Probability Spaces Driven by Geometric Constraints

Randomization, Neutrality, and Fairness October 23, 2023 - October 27, 2023

October 23, 2023 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Wesley Pegden (Carnegie Mellon University)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Probability Spaces Driven by Geometric Constraints

Abstract

What can we understand about probability spaces on "nice" partitions of a geometric region?  Can we design efficient samplers? Can we at least detect extreme outliers?  These questions have become particularly salient in the past several years as the techniques developed by mathematicians are now applied to conduct statistical analyses of things like U.S. political districtings.  We will discuss some recent developments on probability spaces defined by geometric constraints, including positive and negative results on the mixing times of relevant Markov chains, Markov chain methods which eschew mixing-time requirements, and direct sampling methods.

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Probability Spaces Driven by Geometric Constraints

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