Results 1 to 10 of about 5,000 (119)
Connecting choice functions and sets of desirable gambles [PDF]
, 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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Axiomatising Incomplete Preferences through Sets of Desirable Gambles [PDF]
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 ...
Zaffalon, M., Miranda Menéndez, Enrique
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Exchangeability for sets of desirable gambles [PDF]
, 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 +3 more sources
Independent natural extension for sets of desirable gambles [PDF]
, 2011 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. We provide formulas for the smallest such joint, called their independent natural extension, and study its main properties.
de Cooman, Gert, Miranda, Enrique
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Credal networks under epistemic irrelevance using sets of desirable gambles [PDF]
, 2013 We present a new approach to credal networks, which are graphical models that generalise Bayesian nets to deal with imprecise probabilities. Instead of applying the commonly used notion of strong independence, we replace it by the weaker notion of epistemic irrelevance.
De Bock, Jasper, de Cooman, Gert
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Results about sets of desirable gamble sets
Coherent 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.
Campbell-Moore, Catrin
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Infinite Exchangeability for Sets of Desirable Gambles [PDF]
, 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.
de Cooman, Gert, Quaeghebeur, Erik
openaire +2 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.
de Cooman, Gert, Quaeghebeur, Erik
openaire +3 more sources
Lexicographic choice functions [PDF]
, 2017 We investigate a generalisation of the coherent choice functions considered by Seidenfeld et al. (2010), by sticking to the convexity axiom but imposing no Archimedeanity condition. We define our choice functions on vector spaces of options, which allows
de Cooman, Gert +2 more
core +4 more sources
Believing Probabilistic Contents: On the Expressive Power and Coherence of Sets of Sets of Probabilities [PDF]
, 2019 Moss (2018) argues that rational agents are best thought of not as having degrees of belief in various propositions but as having beliefs in probabilistic contents, or probabilistic beliefs.
Campbell-Moore, Catrin, Konek, Jason
core +3 more sources