Conjunction, Disjunction and Iterated Conditioning of Conditional Events (bibtex)
by Angelo Gilio, Giuseppe Sanfilippo
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.
Reference:
Angelo Gilio, Giuseppe Sanfilippo, "Conjunction, Disjunction and Iterated Conditioning of Conditional Events", Chapter in Synergies of Soft Computing and Statistics for Intelligent Data Analysis, Advances in Intelligent Systems and Computing, Springer Berlin Heidelberg, vol. 190, pp. 399-407, 2013. ([A version similar to the published paper])
Bibtex Entry:
@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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