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

Tutorial talk for the Categorical Probability and Statistics workshop 2020:
http://perimeterinstitute.ca/personal...

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,    • Categorical probability theory  
nLab article, https://ncatlab.org/nlab/show/probabi...
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...
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.