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Aggregating Referee Scores: an Algebraic Approach
"... This paper presents a quantitative solution to the problem of aggregating referee scores for manuscripts submitted to peerreviewed conferences or scientific journals. The proposed approach is a particular application of the DempsterShafer theory to a restricted setting, from which an interesting a ..."
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This paper presents a quantitative solution to the problem of aggregating referee scores for manuscripts submitted to peerreviewed conferences or scientific journals. The proposed approach is a particular application of the DempsterShafer theory to a restricted setting, from which an interesting algebraic framework results. The paper investigates the algebraic properties of this framework and shows how to apply it to the score aggregation and document ranking problems. Our scheme is intended to support the paper selection process of a conference or journal, not to replace it. 1
Two kadditive generalizations of the pignistic transform for imprecise decision making
"... The Transferable Belief approach to the Theory of Evidence is based on the pignistic transform which, mapping belief functions to probability distributions, allows to make “precise ” decisions on a set of disjoint hypotheses via classical utility theory. In certain scenarios, however, such as medica ..."
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The Transferable Belief approach to the Theory of Evidence is based on the pignistic transform which, mapping belief functions to probability distributions, allows to make “precise ” decisions on a set of disjoint hypotheses via classical utility theory. In certain scenarios, however, such as medical diagnosis, the need for an “imprecise ” approach to decision making arises, in which sets of possible outcomes are compared. We propose here a framework for imprecise decision derived from the TBM, in which belief functions are mapped to kadditive belief functions (i.e., belief functions whose focal elements have maximal cardinality equal to k) rather than Bayesian ones. We do so by introducing two alternative generalizations of the pignistic transform to the case of kadditive belief functions. The latter has several interesting properties: depending on which properties are deemed the most important, the two distinct generalizations arise. The proposed generalized transforms are empirically validated by applying them to imprecise decision in concrete pattern recognition problems.
Credal semantics of Bayesian transformations in terms of probability intervals
 Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on
, 2010
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Credal semantics of Bayesian transformations
"... In this paper we propose a credal representation of the set of interval probabilities associated with a belief function, and show how it relates to several classical Bayesian transformations of belief functions through the notion of “focus ” of a pair of simplices. Starting from the interpretation o ..."
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In this paper we propose a credal representation of the set of interval probabilities associated with a belief function, and show how it relates to several classical Bayesian transformations of belief functions through the notion of “focus ” of a pair of simplices. Starting from the interpretation of the pignistic function as the center of mass of the credal set of consistent probabilities, we prove that relative belief and plausibility of singletons and intersection probability can be described as foci of different pairs of simplices in the simplex of all probability measures. Such simplices are associated with the lower and upper probability constraints, respectively. This paves the way for the formulation of frameworks similar to the transferable belief model for lower, upper, and interval constraints.
The Intersection Probability and Its Properties
"... Abstract. In this paper we discuss the properties of the intersection probability, a recent Bayesian approximation of belief functions introduced by geometric means. We propose a rationale for this approximation valid for interval probabilities, study its geometry in the probability simplex with res ..."
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Abstract. In this paper we discuss the properties of the intersection probability, a recent Bayesian approximation of belief functions introduced by geometric means. We propose a rationale for this approximation valid for interval probabilities, study its geometry in the probability simplex with respect to the polytope of consistent probabilities, and discuss the way it relates to important operators acting on belief functions. 1
Preface
, 2009
"... All rights reserved. The copyright on each of the papers published in these proceedings remains with the author(s). No part of these proceedings may be reprinted or reproduced or utilised in any form by any electronic, mechanical, or other means without permission in writing from the relevant author ..."
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All rights reserved. The copyright on each of the papers published in these proceedings remains with the author(s). No part of these proceedings may be reprinted or reproduced or utilised in any form by any electronic, mechanical, or other means without permission in writing from the relevant author(s). This book was typeset using L ATEX. Contents
Credal semantics of Bayesian approximations in
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