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EnglishStarting 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.
Gilio, A., & Sanfilippo, G. (2013). Conjunction, disjunction and iterated conditioning of conditional events. In R. Kruse, M.R. Berthold, C. Moewes, M.A. Gil, P. Grzegorzewski, & O. Hryniewicz (a cura di), Synergies of soft computing and statistics for intelligent data analysis (pp. 399-407). Berlin : Springer [10.1007/978-3-642-33042-1_43].
| Data di pubblicazione: | 2013 | |
| Titolo: | Conjunction, disjunction and iterated conditioning of conditional events | |
| Autori: | ||
| Citazione: | Gilio, A., & Sanfilippo, G. (2013). Conjunction, disjunction and iterated conditioning of conditional events. In R. Kruse, M.R. Berthold, C. Moewes, M.A. Gil, P. Grzegorzewski, & O. Hryniewicz (a cura di), Synergies of soft computing and statistics for intelligent data analysis (pp. 399-407). Berlin : Springer [10.1007/978-3-642-33042-1_43]. | |
| 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. | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/978-3-642-33042-1_43 | |
| Settore Scientifico Disciplinare: | Settore MAT/06 - Probabilita' E Statistica Matematica Settore SECS-S/01 - Statistica | |
| Appare nelle tipologie: | 2.01 Capitolo o Saggio |
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http://hdl.handle.net/10447/66129
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