Tutorial: What is a probability monad? (Paolo Perrone)

Tutorial talk for the Categorical Probability and Statistics workshop 2020: http://perimeterinstitute.ca/personal/tfritz/2019/cps_workshop/ Title: What is a probability monad? Speaker: Paolo Perrone Topics: - Basic intuition for monads - Basic intuition for probability monads (starting at 08:10) - The distribution monad (starting at 13:45) - The Giry monad (starting at 18:25) - Overview of other probability monads (starting at 28:25) - Joints and marginals (starting at 31:30) - Some references and further reading (starting at 39:05) More introductory material on probability monads: - Arthur Parzygnat's video series, https://www.youtube.com/playlist?list=PLSx1kJDjrLRSKKHj4zetTZ45pVnGCRN80 - nLab article, https://ncatlab.org/nlab/show/probability+monad - Paolo Perrone, Notes on Category Theory with examples from basic mathematics, especially Chapter 5. https://arxiv.org/abs/1912.10642 - Paolo Perrone, Categorical Probability and Stochastic Dominance in Metric Spaces, PhD thesis, especially Chapter 1. http://www.paoloperrone.org/phdthesis.pdf - Tobias Fritz and Paolo Perrone, Monads, partial evaluations, and rewriting, especially Section 6. https://arxiv.org/abs/1810.06037 See the references at the end of the nLab page for more, and for more research-level material.