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.

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].

### Conjunction, disjunction and iterated conditioning of conditional events

#### 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.
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2013
Settore MAT/06 - Probabilita' E Statistica Matematica
Settore SECS-S/01 - Statistica
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10447/66129`