As a spinoff of the workshop Categorical Probability and Statistics, Oliver Shetler has organized a reading group on category theory applied to statistics. The first meeting is Saturday June 27th at 17:00 UTC.
You can sign up for the group here, and also read more about it there. We’re discussing the group on the Category Theory Community Server, so if you want to join the reading group should probably also join that.
Here is a reading list. I’m sure the group won’t cover all these papers—we’ll start with the first one and see how it goes from there. But it’s certainly helpful to have a list like this.
• McCullagh, What is a statistical model?
• Morse and Sacksteder, Statistical isomorphism.
• Simpson, Probability sheaves and the Giry monad.
• Jacobs, Probabilities, distribution monads, and convex categories.
• Keimel, The monad of probability measures over compact ordered spaces and its Eilenberg-Moore algebras.
• McCullaugh, Di Nardo, Senato, Natural statistics for spectral samples.
• Perrone, Categorical Probability and Stochastic Dominance in Metric Spaces. (Ph.D. thesis)
• Patterson, The Algebra and Machine Representation of Statistical Models. (Ph.D. thesis)
• Tuyeras, A category theoretical argument for causal inference.
• Culbertson and Sturtz, A categorical foundation for Bayesian probability.
• Fong, Causal Theories: A Categorical Perspective on Bayesian Networks. (Masters thesis)
• Fritz and Perrone, A probability monad as the colimit of spaces of finite samples.
• Fritz and Perrone, Bimonoidal structure of probability monads.
• Fritz, A presentation of the category of stochastic matrices.
• Jacobs and Furber, Towards a categorical account of conditional probability.
• Bradley, At the Interface of Algebra and Statistics. (Ph.D. Thesis)
• Bradley, Stoudenmire and Terilla, Modeling sequences with quantum states.
• Jacobs, Categorical aspects of parameter learning.
• Jacobs, Parameters and parameterization in specification, using distributive categories.
• Parzygnat, Inverses, disintegrations, and Bayesian inversion in quantum Markov categories.
Azimuth 
I think it is not just a question of ‘interest’. With Covid there is increasing demands on time. Not so much for me but I see a lot of comments about the new modes of teaching on-line.
I agree with John that trying to bridge the gap between Statistics and areas such as category theory may be very useful.
I’m pretty sure that enough people want to join this reading group that it will take off, despite COVID-19 and other problems.
I was not doubting that but it is the time element. I hope it is very successful as I think that the interplay of category theory with a whole lot of probabilistic and statistical problems could be very important in the future.
Who should we contact for account reactivation? I can’t get into the zulip forum anymore to follow the discussion. Thank you.
Sorry, I don’t know anyone in charge of account reactivation. Accounts usually don’t get deactivated, I think. Maybe the easiest thing is to create a new account.
I tried, but that directs you to a page saying you need an invitation without giving a link or contact address. Who sends out the invitation to join the zulip?
Given the recent talk of inclusion and broadening the community I wonder why the forum needs to be closed anyway – at least for reading if not for posting. Shouldn’t it be easier for people to join?
It’s quite easy. In my blog article here it says “If you want to join this reading group you can register for the Category Theory Community Server and then go here.” So just do that.
Thanks for all the great links. I love reading about folks who are thinking about statistics and probability algebraically. One thing I have always wondered is if there is some category in which you can do statistics, and an associated category that maps those calculations to statements. I’m always fascinated by the precise but seemingly convoluted logic of statistics, as in, we can not say that H1 is true, only that our calculations of a certain probability allows us to reject the validity of some Null hypothesis. This is the language of modern science. We don’t prove a hypothesis is true, only that all competing hypothesis are wrong. Well, casually, we we just say, H1 is true. It all has the feeling of the logic the Bell uses in his calculus with infinitesimals book, constructive logic.
By the way, the obsessive focus on null hypotheses and significance testing is a mistake. People are slowly switching to better methodologies. I wish there were a free online version of Rindskopf’s paper Null-hypothesis tests are not completely stupid, but Bayesian statistics are better, but I don’t see one. These are free:
• Bruno Lecoutre, The significance test controversy and the Bayesian alternative, Encyclopedia of Mathematics.
• Jeffrey A. Gliner, Nancy L. Leech and George A, Morgan, Problems with null hypothesis significance testing (NHST): what do the textbooks say?
The first meeting of the Categorical Statistics Group is Saturday June 27th at 17:00 UTC. You can sign up here, and also read more about it there.