The language and constructions of category theory have proven useful in unifying disparate fields of study and bridging formal gaps between approaches, so it is natural that a categorial eye should be turned to the theory of probability and its relation to formal logic. Continuing from the foundational work of Lawvere and Giry in developing a functorial theory of probability, Stuartz and Culbertson detail the central importance of and connection between deterministic processes and stochastic processes. Fong expanded this theory to give a categorical account of Bayesian causality. Here we collect and summarize the rich body of research in categorical probability theory, and further develop mathematical machinery for applications in algorithmic Bayesian statistics.
Worcester Polytechnic Institute
Major Qualifying Project