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Statistical Inference from Ill-known Data Using Belief Functions

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Uncertainty Analysis in Econometrics with Applications

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 200))

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Abstract

As a general formalism for uncertain reasoning, the theory of belief functions extends the logical and probabilistic approaches to uncertainty: a belief function (or a completely monotone Choquet capacity) can be seen both as a non additive measure and as a generalized set. In this paper, the theory of belief functions is argued to be a suitable framework for statistical analysis of low quality, i.e., imprecise and/or partially reliable data. After a reminder of general concepts of the theory, we show how this approach can be applied to statistical inference by viewing the normalized likelihood function as defining a consonant belief function. The links with likelihood-based and Bayesian inference are discussed.We then show how this method can be extended to the analysis of uncertain data. The approach is illustrated using a running example.

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Authors and Affiliations

  1. UMR CNRS 7253 Heudiasyc, Université de Technologie de Compiègne, BP 20529, F-60205, Compiègne cedex, France

    Thierry Denœux

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  1. Thierry Denœux
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Correspondence to Thierry Denœux .

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Editors and Affiliations

  1. Science and Technology, School of Knowledge Science, Japan Advanced Institute of, Asahidai, Nomi 1-1, Ishikawa, 923-1292, Japan

    Van-Nam Huynh

  2. , Department of Computer Science, University of Texas at El Paso, W. University 500, El Paso, 79968, Texas, USA

    Vladik Kreinovich

  3. , Faculty of Economics, Chiang Mai University, Chinag Mai, 50200, Thailand

    Songsak Sriboonchitta

  4. , Faculty of Economics, Chiang Mai University, Chinag Mai, 50200, Thailand

    Komsan Suriya

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Denœux, T. (2013). Statistical Inference from Ill-known Data Using Belief Functions. In: Huynh, VN., Kreinovich, V., Sriboonchitta, S., Suriya, K. (eds) Uncertainty Analysis in Econometrics with Applications. Advances in Intelligent Systems and Computing, vol 200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35443-4_3

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  • DOI: https://doi.org/10.1007/978-3-642-35443-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35442-7

  • Online ISBN: 978-3-642-35443-4

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