
From imprecise probability assessments to conditional probabilities with quasi additive classes of conditioning events
In this paper, starting from a generalized coherent (i.e. avoiding unifo...
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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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Monitoring Event Frequencies
The monitoring of event frequencies can be used to recognize behavioral ...
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Marginalization in Composed Probabilistic Models
Composition of lowdimensional distributions, whose foundations were lai...
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On compatibility/incompatibility of two discrete probability distributions in the presence of incomplete specification
Conditional specification of distributions is a developing area with man...
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On the Impossibility of Learning the Missing Mass
This paper shows that one cannot learn the probability of rare events wi...
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Identification of Probabilities
Within psychology, neuroscience and artificial intelligence, there has b...
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Predictive distributions that mimic frequencies over a restricted subdomain (expanded preprint version)
A predictive distribution over a sequence of N+1 events is said to be "frequency mimicking" whenever the probability for the final event conditioned on the outcome of the first N events equals the relative frequency of successes among them. Infinitely extendible exchangeable distributions that universally inhere this property are known to have several annoying concomitant properties. We motivate frequency mimicking assertions over a limited subdomain in practical problems of finite inference, and we identify their computable coherent implications. We provide some computed examples using reference distributions, and we introduce computational software to generate any specification. The software derives from an inversion of the finite form of the exchangeability representation theorem. Three new theorems delineate the extent of the usefulness of such distributions, and we show why it may not be appropriate to extend the frequency mimicking assertions for a specified value of N to any arbitrary larger size of N. The constructive results identify the source and structure of "adherent masses" in the limit of a sequence of finitely additive distributions. Appendices develop a novel geometrical representation of conditional probabilities which illuminate the analysis.
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