
Conditional probability in Renyi spaces
In 1933 Kolmogorov constructed a general theory that defines the modern ...
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An Inversion Tool for Conditional Term Rewriting Systems – A Case Study of Ackermann Inversion
We report on an inversion tool for a class of oriented conditional const...
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Statistics with improper posteriors
In 1933 Kolmogorov constructed a general theory that defines the modern ...
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On the proper treatment of improper distributions
The axiomatic foundation of probability theory presented by Kolmogorov h...
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User Interface Tools for Navigation in Conditional Probability Tables and Elicitation of Probabilities in Bayesian Networks
Elicitation of probabilities is one of the most laborious tasks in build...
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Hypothetical revision and matteroffact supposition
The paper studies the notion of supposition encoded in nonArchimedean c...
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Standard State Space Models of Unawareness (Extended Abstract)
The impossibility theorem of Dekel, Lipman and Rustichini has been thoug...
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Disintegration and Bayesian Inversion, Both Abstractly and Concretely
The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measuretheoretic probability  via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several nontrivial examples.
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