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Infinite Exchangeability for Sets of Desirable Gambles [PDF]
Communications in Computer and Information Science, 2010 Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We study infinite exchangeability assessments for them, and give a counterpart of de Finetti’s infinite representation theorem.
Gert De Cooman +2 more
exaly +3 more sources
Exchangeability and sets of desirable gambles
International Journal of Approximate Reasoning, 2012 Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments for them, and prove counterparts of de Finetti's finite and infinite representation theorems.
Gert De Cooman, Erik Quaeghebeur
exaly +4 more sources
Sets of desirable gambles: Conditioning, representation, and precise probabilities
International Journal of Approximate Reasoning, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Inés Couso, Serafin Moral
exaly +2 more sources
Credal networks under epistemic irrelevance: The sets of desirable gambles approach
International Journal of Approximate Reasoning, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gert De Cooman, Jasper de Bock
exaly +4 more sources
Axiomatising Incomplete Preferences through Sets of Desirable Gambles
Journal of Artificial Intelligence Research, 2017 We establish the equivalence of two very general theories: the first is the decision-theoretic formalisation of incomplete preferences based on the mixture independence axiom; the second is the theory of coherent sets of desirable gambles (bounded variables) developed in the context of imprecise probability and extended here to vector-valued gambles ...
Marco Zaffalon, Enrique Miranda 0001
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Irrelevant and independent natural extension for sets of desirable gambles
Journal of Artificial Intelligence Research, 2012 The results in this paper add useful tools to the theory of sets of desirable gambles, a growing toolbox for reasoning with partial probability assessments. We investigate how to combine a number of marginal coherent sets of desirable gambles into a joint set using the properties of epistemic irrelevance and independence.
Gert de Cooman, Enrique Miranda 0001
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A polarity theory for sets of desirable gambles
, 2017 Coherent sets of almost desirable gambles and credal sets are known to be equivalent models. That is, there exists a bijection between the two collections of sets preserving the usual operations, e.g. conditioning. Such a correspondence is based on the polarity theory for closed convex cones.
Alessio Benavoli +3 more
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Connecting choice functions and sets of desirable gambles
, 2014 We study Seidenfeld, Schervish, and Kadane’s notion of choice functions, and want to make them accessible to people who are familiar with sets of desirable gambles. We relate both theories explicitly using their derived strict partial orderings. We give an expression for the most conservative extension of a set of desirable gambles to a choice function.
Van Camp, Arthur +2 more
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Results about sets of desirable gamble sets
CoRRCoherent sets of desirable gamble sets is used as a model for representing an agents opinions and choice preferences under uncertainty. In this paper we provide some results about the axioms required for coherence and the natural extension of a given set of desirable gamble sets.
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Exchangeability for sets of desirable gambles
, 2009 Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We study exchangeability assessments for such models, and prove a counterpart of de Finetti's finite representation theorem. We show that this representation theorem has a very nice geometrical interpretation.
de Cooman, Gert, Quaeghebeur, Erik
openaire +1 more source