The Logical Postulates of Böge, Carnap and Johnson in the Context of Papangelou Processes

We adapt Johnson’s sufficiency postulate, Carnap’s prediction invariance postulate and Böge’s learn-merge invariance to the context of Papangelou processes and discuss equivalence of their generalizations, in particular their weak and strong generalizations. This discussion identifies a condition wh...

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Bibliographic Details
Published in:Journal of theoretical probability 2015-12, Vol.28 (4), p.1431-1446
Main Authors: Rafler, Mathias, Zessin, Hans
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
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Summary:We adapt Johnson’s sufficiency postulate, Carnap’s prediction invariance postulate and Böge’s learn-merge invariance to the context of Papangelou processes and discuss equivalence of their generalizations, in particular their weak and strong generalizations. This discussion identifies a condition which occurs in the construction of Papangelou processes. In particular, we show that these generalizations characterize classes of Poisson and Pólya point processes.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-014-0543-2