Workshop Categorical Probability and Statistics, 5–8 June 2020 (online)

Probability theory and statistics are traditionally built on measure theory as a foundation. Although this has resulted in rich theoretical developments with enormous practical use, there is a common sentiment that there ought to be a more high-level formalism which abstracts away from measure theory, providing a system of axioms that allows for the development of theorems of higher complexity. Consider software development as an analogy: complex software can be developed in a high-level programming language more easily than directly in terms of machine code.

The problem of finding a high-level framework for the structure of probability and statistics has been pursued independently, with somewhat varying perspectives, by three relatively disjoint communities:

• Theoretical statisticians have proposed more structural perspectives on the foundations of statistics since the 1970s.
• Computer scientists have been developing high-level approaches to probability, motivated by theoretical and practical problems related to probabilistic computation and probabilistic programming.
• Inspired by Lawvere's visionary insights, category theorists also have developed an interest in probability and statistics from a structural angle.

The past few years have seen enormous progress especially by the latter two communities. The time is now ripe for an exchange of results, ideas and methods between all three of these.

Through this workshop, we hope for the emergence of a new interdisciplinary research community on categorical probability and statistics.