There is a lot of recent interesting work on using category theory to talk about Statistics and Probability theory. This goes back to the 60's with Lawvere's work on the Giry Monad.

Interesting People

• Paolo Perrone
• Evan Patterson Look at his PhD thesis.
• Bart Jacobs has been doing some work on category theory and probability. In particular he is writing a book Structured Probabilitistic Reasoning and a draft can be found here

Interesting Online Talks

• Look at the website Applied Category Theory there you will finda link to a workshop on Categorical Probability and Statistics. All the videos of the talks are available online on youtube.