Conjunction, Disjunction and Iterated Conditioning of Conditional Events. Gilio, A. & Sanfilippo, G. In Kruse, R., Berthold, M. R., Moewes, C., Gil, M. A., Grzegorzewski, P., & Hryniewicz, O., editors, Synergies of Soft Computing and Statistics for Intelligent Data Analysis, volume 190, of Advances in Intelligent Systems and Computing, pages 399-407. Springer Berlin Heidelberg, 2013.
Paper doi abstract bibtex Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we give the lower and upper bounds on the conjunction. We also examine an apparent paradox concerning stochastic independence which can actually be explained in terms of uncorrelation. We briefly introduce the notions of disjunction and iterated conditioning and we show that the usual probabilistic properties still hold.
@INCOLLECTION{2013:5SMPS,
author = {Gilio, Angelo and Sanfilippo, Giuseppe},
title = {Conjunction, Disjunction and Iterated Conditioning of Conditional
Events},
booktitle = {Synergies of Soft Computing and Statistics for Intelligent Data Analysis},
publisher = {Springer Berlin Heidelberg},
year = {2013},
editor = {Kruse, Rudolf and Berthold, Michael R. and Moewes, Christian and
Gil, Maria Angeles and Grzegorzewski, Przemyslaw and Hryniewicz,
Olgierd},
volume = {190},
series = {Advances in Intelligent Systems and Computing},
pages = {399-407},
abstract = {Starting from a recent paper by S. Kaufmann, we introduce a notion
of conjunction of two conditional events and then we analyze it in
the setting of coherence. We give a representation of the conjoined
conditional and we show that this new object is a conditional random
quantity, whose set of possible values normally contains the probabilities
assessed for the two conditional events. We examine some cases of
logical dependencies, where the conjunction is a conditional event;
moreover, we give the lower and upper bounds on the conjunction.
We also examine an apparent paradox concerning stochastic independence
which can actually be explained in terms of uncorrelation. We briefly
introduce the notions of disjunction and iterated conditioning and
we show that the usual probabilistic properties still hold.},
comment = {<a href="http://www.unipa.it/giuseppe.sanfilippo/pdf/2013/smps2012/smps2012_quasifinal.pdf">[A
version similar to the published paper]</a>},
doi = {10.1007/978-3-642-33042-1_43},
isbn = {978-3-642-33041-4},
issn = {2194-5357},
keywords = {Conditional events; conditional random quantities; conjunction; disjunction;
iterated conditionals},
scopus = {{2-s2.0-84870731187}},
url = {http://dx.doi.org/10.1007/978-3-642-33042-1_43},
wos = {{WOS:000312969600043}}
}
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