0000000000177097
AUTHOR
G. Sanfilippo
Some results on generalized coherence of conditional probability bounds
Based on the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence), we adopt a probabilistic approach to uncertainty based on conditional probability bounds. Our notion of g-coherence is equivalent to the 'avoiding uniform loss' property for lower and upper probabilities (a la Walley). Moreover, given a g-coherent imprecise assessment by our algorithms we can correct it obtaining the associated coherent assessment (in the sense of Walley and Williams). As is well known, the problems of checking g-coherence and propagating tight g-coherent intervals are NP and FP^NP complete, respectively, and thus NP-hard. Two notions which may be helpful to reduce co…
Algebraic aspects and coherence conditions for conjunctions among conditional events
We deepen the study of a notion of conjunction among conditional events, introduced in previous papers in theframework of coherence. This notion of conjunction, differently from other approaches, is given in the setting ofconditional random quantities. We show that some well known properties which are satisfied by conjunctionsof unconditional events are also satisfied by conjunctions of conditional events. In particular we examine anadditive property and a decomposition formula, by also obtaining a generalized inclusion-exclusion formula. Then,by exploiting the notion of conjunction, we introduce the set of constituents generated bynconditional events.Moreover, under logical independence, w…
Generalized Logical Operations among Conditional Events
We generalize, by a progressive procedure, the notions of conjunction and disjunction of two conditional events to the case of $n$ conditional events. In our coherence-based approach, conjunctions and disjunctions are suitable conditional random quantities. We define the notion of negation, by verifying De Morgan's Laws. We also show that conjunction and disjunction satisfy the associative and commutative properties, and a monotonicity property. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals; in particular we examine the Fr'echet-Hoeffding bounds. Moreover, we study the reverse probabilistic inference from the conjunction $mathc…
Generalized coherence and connection property of imprecise conditional previsions.
In this paper we consider imprecise conditional prevision assessments on random quantities with finite set of possible values. We use a notion of generalized coherence which is based on the coherence principle of de Finetti. We consider the checking of g-coherence, by extending some previous results obtained for imprecise conditional probability assessments. Then, we study a connection property of interval-valued gcoherent prevision assessments, by extending a result given in a previous paper for precise assessments.
On general conditional prevision assessments
In this paper we consider general conditional random quantities of the kind $X|Y$, where $X$ and $Y$ are finite discrete random quantities. Then, we introduce the notion of coherence for conditional prevision assessments on finite families of general conditional random quantities. Moreover, we give a compound prevision theorem and we examine the relation between the previsions of $X|Y$ and $Y|X$. Then, we give some results on random gains and, by a suitable alternative theorem, we obtain a characterization of coherence. We also propose an algorithm for the checking of coherence. Finally, we briefly examine the case of imprecise conditional prevision assessments by introducing the notions of…
Compounds of conditionals and iterated conditioning under coherence
We discuss the problem of defining logical operations among conditional events. Differently from many authors, we define the conjunction and disjunction in the setting of conditional random quantities. In probability theory and in probability logic a relevant problem, largely discussed by many authors, is that of defining logical operations among conditional events. In the many works concerning these operations, the conjunction and disjunction have been usually defined as suitable conditional events. In Kaufmann 2009 it has been proposed a theory for the compounds of conditionals which has been framed in the setting of coherence in (Gilio and Sanfilippo , 2013, 2014) In this framework, whic…