### Categorical Statistics Group

#### Posted by John Baez

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, Parameters and parameterization in specification, using distributive categories.

Parzygnat, Inverses, disintegrations, and Bayesian inversion in quantum Markov categories.

## Re: Categorical Statistics Group

I’ve changed this blog article since the Categorical Statistics Group is becoming more real.

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.