Evan Patterson: The algebra of statistical theories and models

MIT Category Theory Seminar
2020/07/23

©Spifong

Speaker: Evan Patterson
Title: The algebra of statistical theories and models

Abstract:
Using tools from categorical logic, a precise analogy is drawn between models in logic and statistics. The notion of a statistical theory is introduced as a small Markov category with extra linear algebraic structure. Models of statistical theories in a category of Markov kernels are then seen to be statistical models, in the conventional sense. Morphisms between statistical theories, and their induced model migration functors, formalize relationships between different statistical models. These ideas are illustrated by a wide range of models from classical applied statistics, such as linear models, mixed models, and generalized linear models.

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[jean-baptistelasselle]

How interesting considering what an equivalence between categories of statistical theories carries... Thank you for sharing publicly ! :)