Statistics for Category Theorists

As a spinoff of the workshop Categorical Probability and Statistics, some people are now batting around the idea of having a reading group on statistics for category theorists. Here is a reading list compiled by Oliver Shetler:

• 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 (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”

• 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”

If you want to join this reading group you can register for the Category Theory Community Server and then go here. I’m sure the group won’t cover all the above papers, and I’m not even sure the group will take off—that depends on how much interest there is. But it’s certainly helpful to have a list like this.