Statistical models as natural transformations: meaningfulness, coherence and priors as states in Markov categories
作为自然变换的统计模型:马尔可夫范畴中的有意义性、协调性与先验状态
We show that a statistical model in the sense of McCullagh, in the form given by Brøns, is a natural transformation between two functors from the category of designs to the Kleisli category Stoch of the Giry monad, provided that its components are measurable in the parameter. The condition is empty for finite models. A design-indexed quantity is a family of morphisms of Stoch defined on the parameter objects, called meaningful if it is natural. We prove that Tjur's…