Stochastic maps - 04 -Bayes' theorem

We finally state Bayes' theorem in a categorical language. This version of the theorem states that given a measure-preserving stochastic map, there exists a measure-preserving stochastic map in the opposite direction that satisfies a diagrammatic condition equivalent to Bayes' rule. This Bayesian inverse is unique almost surely.

This is part of a series of lectures on special topics in linear algebra. It is assumed the viewer has taken (or is well into) a course in linear algebra. Some topics may also require additional background. Topics covered include linear regression and data analysis, ordinary linear differential equations, differential operators, function spaces, category-theoretic aspects of linear algebra, support vector machines (machine learning), Hamming's error-correcting codes, stochastic maps and Markov chains, tensor products, finite-dimensional C*-algebras, algebraic probability theory, completely positive maps, aspects of quantum information theory, and more.

These videos were created during the 2019 Spring/Summer semester at the UConn CETL Lightboard Room.

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