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GIUSEPPE SANFILIPPO

Lower and Upper Probability Bounds for Some Conjunctions of Two Conditional Events

  • Autori: Giuseppe Sanfilippo
  • Anno di pubblicazione: 2018
  • Tipologia: Contributo in atti di convegno pubblicato in volume (Capitolo o saggio)
  • OA Link: http://hdl.handle.net/10447/302431

Abstract

In this paper we consider, in the framework of coherence, four different definitions of conjunction among conditional events. In each of these definitions the conjunction is still a conditional event. We first recall the different definitions of conjunction; then, given a coherent probability assessment (x, y) on a family of two conditional events {A|H,B|K}, for each conjunction (A|H)∧(B|K) we determine the (best) lower and upper bounds for the extension z=P[(A|H)∧(B|K)]. We show that, in general, these lower and upper bounds differ from the classical Fréchet-Hoeffding bounds. Moreover, we recall a notion of conjunction studied in recent papers, such that the result of conjunction of two conditional events A|H and B|K is (not a conditional event, but) a suitable conditional random quantity, with values in the interval [0, 1]. Then, we remark that for this conjunction, among other properties, the Fréchet-Hoeffding bounds are preserved.