2,642 research outputs found
Decision-Making with Belief Functions: a Review
Approaches to decision-making under uncertainty in the belief function
framework are reviewed. Most methods are shown to blend criteria for decision
under ignorance with the maximum expected utility principle of Bayesian
decision theory. A distinction is made between methods that construct a
complete preference relation among acts, and those that allow incomparability
of some acts due to lack of information. Methods developed in the imprecise
probability framework are applicable in the Dempster-Shafer context and are
also reviewed. Shafer's constructive decision theory, which substitutes the
notion of goal for that of utility, is described and contrasted with other
approaches. The paper ends by pointing out the need to carry out deeper
investigation of fundamental issues related to decision-making with belief
functions and to assess the descriptive, normative and prescriptive values of
the different approaches
Valid and efficient imprecise-probabilistic inference with partial priors, II. General framework
Bayesian inference requires specification of a single, precise prior
distribution, whereas frequentist inference only accommodates a vacuous prior.
Since virtually every real-world application falls somewhere in between these
two extremes, a new approach is needed. This series of papers develops a new
framework that provides valid and efficient statistical inference, prediction,
etc., while accommodating partial prior information and imprecisely-specified
models more generally. This paper fleshes out a general inferential model
construction that not only yields tests, confidence intervals, etc.~with
desirable error rate control guarantees, but also facilitates valid
probabilistic reasoning with de~Finetti-style no-sure-loss guarantees. The key
technical novelty here is a so-called outer consonant approximation of a
general imprecise probability which returns a data- and partial prior-dependent
possibility measure to be used for inference and prediction. Despite some
potentially unfamiliar imprecise-probabilistic concepts in the development, the
result is an intuitive, likelihood-driven framework that will, as expected,
agree with the familiar Bayesian and frequentist solutions in the respective
extreme cases. More importantly, the proposed framework accommodates partial
prior information where available and, therefore, leads to new solutions that
were previously out of reach for both Bayesians and frequentists. Details are
presented here for a wide range of examples, with more practical details to
come in later installments.Comment: Follow-up to arXiv:2203.06703. Feedback welcome at
https://researchers.one/articles/22.11.0000
Idempotent conjunctive combination of belief functions: Extending the minimum rule of possibility theory.
IATE : Axe 5 Application intégrée de la connaissance, de l’information et des technologies permettant d’accroître la qualité et la sécurité des aliments Contact : [email protected] (S. Destercke), [email protected] (D. Dubois) Fax: +33 0 4 9961 3076.International audienceWhen conjunctively merging two belief functions concerning a single variable but coming from different sources, Dempster rule of combination is justified only when information sources can be considered as independent. When dependencies between sources are ill-known, it is usual to require the property of idempotence for the merging of belief functions, as this property captures the possible redundancy of dependent sources. To study idempotent merging, different strategies can be followed. One strategy is to rely on idempotent rules used in either more general or more specific frameworks and to study, respectively, their particularisation or extension to belief functions. In this paper, we study the feasibility of extending the idempotent fusion rule of possibility theory (the minimum) to belief functions. We first investigate how comparisons of information content, in the form of inclusion and least-commitment, can be exploited to relate idempotent merging in possibility theory to evidence theory. We reach the conclusion that unless we accept the idea that the result of the fusion process can be a family of belief functions, such an extension is not always possible. As handling such families seems impractical, we then turn our attention to a more quantitative criterion and consider those combinations that maximise the expected cardinality of the joint belief functions, among the least committed ones, taking advantage of the fact that the expected cardinality of a belief function only depends on its contour function
On various ways of tackling incomplete information in statistics
International audienceThis short paper discusses the contributions made to the featured section on Low Quality Data. We further refine the distinction between the ontic and epistemic views of imprecise data in statistics. We also question the extent to which likelihood functions can be viewed as belief functions. Finally we comment on the data disambiguation effect of learning methods, relating it to data reconciliation problems
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