
A Topological Proof of Sklar's Theorem in Arbitrary Dimensions
We prove Sklar's theorem in infinite dimensions via a topological argume...
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Projective Limit Random Probabilities on Polish Spaces
A pivotal problem in Bayesian nonparametrics is the construction of prio...
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A Counter Example to Theorems of Cox and Fine
Cox's wellknown theorem justifying the use of probability is shown not ...
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A Structural Approach to CoordinateFree Statistics
We consider the question of learning in general topological vector space...
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Representable Markov Categories and Comparison of Statistical Experiments in Categorical Probability
Markov categories are a recent categorical approach to the mathematical ...
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Posterior distribution existence and error control in Banach spaces
We generalize the results of Christen2017 on expected Bayes factors (BF)...
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Algorithmically Optimal Outer Measures
We investigate the relationship between algorithmic fractal dimensions a...
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Copula Measures and Sklar's Theorem in Arbitrary Dimensions
Although copulas are used and defined for various infinitedimensional objects (e.g. Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies these concepts. We propose a unified approach and define copulas as probability measures on general product spaces. For this we prove Sklar's Theorem in this infinitedimensional setting. We show how to transfer this result to various function space settings and describe how to model and approximate dependent probability measures in these spaces in the realm of copulas.
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