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Theory of evidence  a survey of its mathematical foundations, applications and computational aspects
 ZOR MATHEMATICAL METHODS OF OPERATIONS RESEARCH
, 1994
"... The mathematical theory of evidence has been introduced by Glenn Shafer in 1976 as a new approach to the representation of uncertainty. This theory can be represented under several distinct but more or less equivalent forms. Probabilistic interpretations of evidence theory have their roots in Arthur ..."
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The mathematical theory of evidence has been introduced by Glenn Shafer in 1976 as a new approach to the representation of uncertainty. This theory can be represented under several distinct but more or less equivalent forms. Probabilistic interpretations of evidence theory have their roots in Arthur Dempster's multivalued mappings of probability spaces. This leads to random set and more generally to random lter models of evidence. In this probabilistic view evidence is seen as more or less probable arguments for certain hypotheses and they can be used to support those hypotheses to certain degrees. These degrees of support are in fact the reliabilities with which the hypotheses can be derived from the evidence. Alternatively, the mathematical theory of evidence can be founded axiomatically on the notion of belief functions or on the allocation of belief masses to subsets of a frame of discernment. These approaches aim to present evidence theory as an extension of probability theory. Evidence theory has been used to represent uncertainty in expert systems, especially in the domain of diagnostics. It can be applied to decision analysis and it gives a new perspective for statistical analysis. Among its further applications are image processing, project planing and scheduling and risk analysis. The computational problems of evidence theory
An ObjectOriented Architecture for Possibilistic Models
 in: Proc. 1994 Conf. ComputerAided Systems Technology
, 1994
"... . An architecture for the implementation of possibilistic models in an objectoriented programming environment (C++ in particular) is described. Fundamental classes for special and general random sets, their associated fuzzy measures, special and general distributions and fuzzy sets, and possibilist ..."
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. An architecture for the implementation of possibilistic models in an objectoriented programming environment (C++ in particular) is described. Fundamental classes for special and general random sets, their associated fuzzy measures, special and general distributions and fuzzy sets, and possibilistic processes are specified. Supplementary methodsincluding the fast Mobius transform, the maximum entropy and Bayesian approximations of random sets, distribution operators, compatibility measures, consonant approximations, frequency conversions, and possibilistic normalization and measurement methodsare also introduced. Empirical results to be investigated are also described. 1 Introduction Possibility theory [4] is an alternative information theory to that based on probability. Although possibility theory is logically independent of probability theory, they are related: both arise in DempsterShafer evidence theory as fuzzy measures defined on random sets; and their distributions a...
Shared ordered binary decision diagrams for DempsterShafer theory
 in European Conference ECSQARU’07, Hammamet, ser. Lecture Notes in Computer Science
, 2007
"... Abstract. The binary representation is widely used for representing focal sets of DempsterShafer belief functions because it allows to compute efficiently all relevant operations. However, as its space requirement grows exponentially with the number of variables involved, computations may become pr ..."
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Abstract. The binary representation is widely used for representing focal sets of DempsterShafer belief functions because it allows to compute efficiently all relevant operations. However, as its space requirement grows exponentially with the number of variables involved, computations may become prohibitive or even impossible for belief functions with larger domains. This paper proposes shared ordered binary decision diagrams for representing focal sets. This not only allows to compute efficiently all relevant operations, but also turns out to be a compact representation of focal sets. 1
Submitted to the Annals of Applied Statistics ESTIMATING LIMITS FROM POISSON COUNTING DATA USING DEMPSTERSHAFER ANALYSIS
, 812
"... We present a DempsterShafer (DS) approach to estimating limits from Poisson counting data with nuisance parameters. DempsterShafer is a statistical framework that generalizes Bayesian statistics. DS calculus augments traditional probability by allowing mass to be distributed over power sets of the ..."
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We present a DempsterShafer (DS) approach to estimating limits from Poisson counting data with nuisance parameters. DempsterShafer is a statistical framework that generalizes Bayesian statistics. DS calculus augments traditional probability by allowing mass to be distributed over power sets of the event space. This eliminates the Bayesian dependence on prior distributions while allowing the incorporation of prior information when it is available. We use the Poisson DempsterShafer model (DSM) to derive a posterior DSM for the “Banff upper limits challenge ” threePoisson model. The results compare favorably with other approaches, demonstrating the utility of the approach. We argue that the reduced dependence on priors afforded by the DempsterShafer framework is both practically and theoretically desirable. 1. Introduction. This