Upper and Lower Probabilities Induced by a Multivalued Mapping

Dempster, A. P.

doi:10.1214/aoms/1177698950

Cited by 5,723 publications

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“…For example, we thereby avoid the need to constantly make special provision for cases in which denominators are zero. 7 The weighting function ϕ ht is equivalent to a belief function in the Dempster-Shafer theory of evidence (Dempster [9], Shafer [35]). See Appendix B for a brief introduction.…”

Section: Predictionsmentioning

confidence: 99%

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Dynamics of Inductive Inference in a Unified Framework

Gilboa¹,

Samuelson²,

Schmeidler³

2015

Analogies and Theories

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We present a model of inductive inference that includes, as special cases, Bayesian reasoning, case-based reasoning, and rulebased reasoning. This unified framework allows us to examine how the various modes of inductive inference can be combined and how their relative weights change endogenously. For example, we establish conditions under which an agent who does not know the structure of the data generating process will decrease, over the course of her reasoning, the weight of credence put on Bayesian vs. non-Bayesian reasoning. We illustrate circumstances under which probabilistic models are used until an unexpected outcome occurs, whereupon the agent resorts to more basic reasoning techniques, such as case-based and rule-based reasoning, until enough data are gathered to formulate a new probabilistic model.

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Section: Predictionsmentioning

confidence: 99%

“…Finally, the set of singletons contained in a conjecture will also be of interest, and we let E 2 be the σ-algebra generated by all such sets. 9 Summarizing:…”

Section: Predictionsmentioning

confidence: 99%

Dynamics of Inductive Inference in a Unified Framework

Gilboa¹,

Samuelson²,

Schmeidler³

2015

Analogies and Theories

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“…The DS theory, also known as Evidence Theory, was first formulated in the late 1970s by Dempster (1967) and later on extended and formalised by Shafer (1976). DS theory can be used for inference in the presence of incomplete and uncertain information, provided by different, independent, sources.…”

Section: Dempster-shafer Theorymentioning

confidence: 99%

Pipe burst diagnostics using evidence theory

Bicik

Kapelan

Makropoulos

et al. 2010

Journal of Hydroinformatics

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This paper presents a decision support methodology aimed at assisting Water Distribution System (WDS) operators in the timely location of pipe bursts. This will enable them to react more systematically and promptly. The information gathered from various data sources to help locate where a pipe burst might have occurred is frequently conflicting and imperfect. The methodology developed in this paper deals effectively with such information sources. The raw data collected in the field is first processed by means of several models, namely the pipe burst prediction model, the hydraulic model and the customer contacts model. The Dempster-Shafer Theory of Evidence is then used to combine the outputs of these models with the aim of increasing the certainty of determining the location of a pipe burst within a WDS. This new methodology has been applied to several semi-real case studies. The results obtained demonstrate that the method shows potential for locating the area of a pipe burst by capturing the varying credibility of the individual models based on their historical performance.

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“…As it seems, we have to choose between two alternatives, both of which have serious drawbacks. (Note that approaches like storing the possibility measure instead of the basic possibility assignment-which is the approach underlying the so-called Dempster-Shafer theory [Dempster 1967, Dempster 1968, Shafer 1976]-or trying to represent the contexts explicitly are clearly out of the question, because for problems in the real world both approaches require too much storage space.) In the first place, we could try to stick to the standard way of completing a possibility measure from a basic possibility assignment, namely by taking the maximum over the ele-mentary events.…”

Section: Possibility Measuresmentioning

confidence: 99%