TITLE: Category theory and statistics
QUESTION [10 upvotes]: I've been juggling with some concepts from statistics revolving around properties of estimators and sufficient statistics, and I can't help but notice that they have a strong categorical flavor, e.g. I'm pretty sure minimal sufficient statistics are terminal objects in an appropriate category.
I know someone must have worked these things out but haven't been able to find it - I'd be grateful if someone could give me a pointer to some illuminating discussion of applications of category theory to statistics.

REPLY [2 votes]: The following paper of T. Fritz seems to be close to what you're after, arXiv:1908.01021. In particular the sections 14-15-16.