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

Tutorial talk for the Categorical Probability and Statistics workshop 2020:

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:

See the references at the end of the nLab page for more, and for more research-level material.

[NikolajKuntner]

Thank you for this nice introduction!
I wonder if we don't require too much of our structure here if we want things to work for all objects. Usually, in hands on probability applications, one is just a few spaces.

[TheGastricPigeon]

I think that there is a typo on slide 16. Chapman-Kolmogorov should be the sum over Y of k(x, y) h(y, z); not k(x, y) k(y, z)

[haydenkwon]

This is a sweet way to think about it thanks dawg