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تسجيل مستخدم جديدDe Finettis Theorem in Categorical Probability
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We present a novel proof of de Finettis Theorem characterizing permutation-invariant probability measures of infinite sequences of variables, so-called exchangeable measures. The proof is phrased in the language of Markov categories, which provide an abstract categorical framework for probability and information flow. The diagrammatic and abstract nature of the arguments makes the proof intuitive and easy to follow. We also show how the usual measure-theoretic version of de Finettis Theorem for standard Borel spaces is an instance of this result.
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A sequence of random variables is called exchangeable if the joint distribution of the sequence is unchanged by any permutation of the indices. De Finettis theorem characterizes all ${0,1}$-valued exchangeable sequences as a mixture of sequences of i
ndependent random variables. We present an new, elementary proof of de Finettis Theorem. The purpose of this paper is to make this theorem accessible to a broader community through an essentially self-contained proof.
Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this approach is advanced by stating and proving equivalent conditions for second-order stochastic dominance, a widely used way o
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This paper reformulates a classical result in probability theory from the 1930s in modern categorical terms: de Finettis representation theorem is redescribed as limit statement for a chain of finite spaces in the Kleisli category of the Giry monad.
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