2016/11/11 by Takanori Adachi, Adachi, Takanori, Yoshihiro Ryu +1 · 1 citation
Computer Science · Decision Sciences · #16B50 #18B99 #60A99 #60G20 #Bayesian Modeling and Causal Inference #Decision-Making and Behavioral Economics #FOS: Mathematics #Probability (math.PR) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.1611.03630
openalex publication_date 2016/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a category Prob of probability spaces whose objects are all probability spaces and arrows are corresponding to measurable functions satisfying an absolutely continuous requirement. We can consider a Prob-arrow as an evolving direction of information with a way of its interpretation. We introduce a contravariant functor E from Prob to Set, the category of sets. The functor E provides conditional expectations along arrows in Prob, which are generalizations of the classical conditional expectations. For a Prob arrow f, we introduce two concepts f-measurability and f-independence and investigate their interaction with conditional expectations along f. We also show that the completion of probability spaces is naturally formulated as an endofunctor of Prob.