2,300 research outputs found
From imprecise probability assessments to conditional probabilities with quasi additive classes of conditioning events
In this paper, starting from a generalized coherent (i.e. avoiding uniform
loss) intervalvalued probability assessment on a finite family of conditional
events, we construct conditional probabilities with quasi additive classes of
conditioning events which are consistent with the given initial assessment.
Quasi additivity assures coherence for the obtained conditional probabilities.
In order to reach our goal we define a finite sequence of conditional
probabilities by exploiting some theoretical results on g-coherence. In
particular, we use solutions of a finite sequence of linear systems.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty
in Artificial Intelligence (UAI2012
The Goodman-Nguyen Relation within Imprecise Probability Theory
The Goodman-Nguyen relation is a partial order generalising the implication
(inclusion) relation to conditional events. As such, with precise probabilities
it both induces an agreeing probability ordering and is a key tool in a certain
common extension problem. Most previous work involving this relation is
concerned with either conditional event algebras or precise probabilities. We
investigate here its role within imprecise probability theory, first in the
framework of conditional events and then proposing a generalisation of the
Goodman-Nguyen relation to conditional gambles. It turns out that this relation
induces an agreeing ordering on coherent or C-convex conditional imprecise
previsions. In a standard inferential problem with conditional events, it lets
us determine the natural extension, as well as an upper extension. With
conditional gambles, it is useful in deriving a number of inferential
inequalities.Comment: Published version:
http://www.sciencedirect.com/science/article/pii/S0888613X1400101
Nonmonotonic Probabilistic Logics between Model-Theoretic Probabilistic Logic and Probabilistic Logic under Coherence
Recently, it has been shown that probabilistic entailment under coherence is
weaker than model-theoretic probabilistic entailment. Moreover, probabilistic
entailment under coherence is a generalization of default entailment in System
P. In this paper, we continue this line of research by presenting probabilistic
generalizations of more sophisticated notions of classical default entailment
that lie between model-theoretic probabilistic entailment and probabilistic
entailment under coherence. That is, the new formalisms properly generalize
their counterparts in classical default reasoning, they are weaker than
model-theoretic probabilistic entailment, and they are stronger than
probabilistic entailment under coherence. The new formalisms are useful
especially for handling probabilistic inconsistencies related to conditioning
on zero events. They can also be applied for probabilistic belief revision.
More generally, in the same spirit as a similar previous paper, this paper
sheds light on exciting new formalisms for probabilistic reasoning beyond the
well-known standard ones.Comment: 10 pages; in Proceedings of the 9th International Workshop on
Non-Monotonic Reasoning (NMR-2002), Special Session on Uncertainty Frameworks
in Nonmonotonic Reasoning, pages 265-274, Toulouse, France, April 200
Default Logic in a Coherent Setting
In this talk - based on the results of a forthcoming paper (Coletti,
Scozzafava and Vantaggi 2002), presented also by one of us at the Conference on
"Non Classical Logic, Approximate Reasoning and Soft-Computing" (Anacapri,
Italy, 2001) - we discuss the problem of representing default rules by means of
a suitable coherent conditional probability, defined on a family of conditional
events. An event is singled-out (in our approach) by a proposition, that is a
statement that can be either true or false; a conditional event is consequently
defined by means of two propositions and is a 3-valued entity, the third value
being (in this context) a conditional probability
Decision-Making in the Context of Imprecise Probabilistic Beliefs
Coherent imprecise probabilistic beliefs are modelled as incomplete comparative likelihood relations admitting a multiple-prior representation. Under a structural assumption of Equidivisibility, we provide an axiomatization of such relations and show uniqueness of the representation. In the second part of the paper, we formulate a behaviorally general axiom relating preferences and probabilistic beliefs which implies that preferences over unambiguous acts are probabilistically sophisticated and which entails representability of preferences over Savage acts in an Anscombe-Aumann-style framework. The motivation for an explicit and separate axiomatization of beliefs for the study of decision-making under ambiguity is discussed in some detail.
Persistent Disagreement and Polarization in a Bayesian Setting
For two ideally rational agents, does learning a finite amount of shared evidence necessitate agreement? No. But does it at least guard against belief polarization, the case in which their opinions get further apart? No. OK, but are rational agents guaranteed to avoid polarization if they have access to an infinite, increasing stream of shared evidence? No
Bivariate p-boxes
A p-box is a simple generalization of a distribution function, useful to study a random number in the presence of imprecision. We propose an extension of p-boxes to cover imprecise evaluations of pairs of random numbers and term them bivariate p-boxes. We analyze their rather weak consistency properties, since they are at best (but generally not) equivalent to 2-coherence. We therefore focus on the relevant subclass of coherent p-boxes, corresponding to coherent lower probabilities on special domains. Several properties of coherent p-boxes are investigated and compared with those of (one-dimensional) p-boxes or of bivariate distribution functions
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