Categories and Probability Theory

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The discussion centers on the intersection of probability theory and category theory, with a specific inquiry into studies that explore probability from a categorical perspective. Participants express a lack of awareness regarding existing literature that directly addresses this relationship, aside from mentions of probabilistic automatons and precategories. There is a call for clarification on what a category-theoretic approach to probability might entail, particularly regarding the definition of objects, morphisms, and natural transformations. The conversation highlights a gap in resources and references on this topic. Overall, the need for more comprehensive studies linking these two fields is evident.
Alamino
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Does anyone know if there is any study of probability theory from the point of view of category theory? I was trying to find some references but I just found something about probabilistic automatons and precategories. I would like to see something about probability distributions and categories. Any references?
 
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I'm not aware of anything that might be described as a category theoretic approach to probability. I wonder what you mean by it, or, rather, what do you envisage might be the objects, morphisms and natural transformations/functors?
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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