Categorical Statistics Group Kickoff (meeting # 0)

UTC Meeting Time: 17:00 UTC
Zoom ID: 807 569 857

We will pick sections to read, and concepts to research. Then, at future meetings, we will spend the bulk of our time fleshing out and documenting one concept at a time. The goal is to keep the workload light so we can show up consistently and make monotonic progress.

This open-to-all reading group was originally inspired by a conference on Categorical Statistics and Probability. People of many backgrounds and levels are welcome.

At this first meeting, no preparation is required, other than to casually peruse our menu of papers. We will just discuss directions and decide which paper to read first (if you want a say on what we read, please show up!).

Please post names of any additional papers people think are relevant here or on the Zulip chat. Ask for an invite if you don't have one, or click the links here: https://johncarlosbaez.wordpress.com/2020/06/10/statistics-for-category-theorists/

Our work will ultimately go here:
https://wiki.functorialwiki.org/act/show/Statistics+reading+group

Links to all the papers are available at either of the above links.

Here is a menu of papers we may read:

McCullagh, “What is a statistical model?”

Morse and Sacksteder - “Statistical isomorphism”

Simpson - “Probability Sheaves and the Giry Monad”

Fritz - “A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics 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” (Pd.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” 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”

Tuyeres, “Category Theory for Genetics I: Mutations and Sequence Alignments”

Parzygnat, “Inverses, Disintegrations, and Bayesian Inversion in Quantum Markov Categories”

Jacobs, “A Channel-Based Perspective on Conjugate Priors”