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Statistical reasoning with set-valued information : Ontic vs. epistemic views

Couso, Inès and Dubois, Didier Statistical reasoning with set-valued information : Ontic vs. epistemic views. (2014) International Journal of Approximate Reasonning, 55 (7). 1502-1518. ISSN 0888-613X

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Official URL: http://dx.doi.org/10.1016/j.ijar.2013.07.002

Abstract

In information processing tasks, sets may have a conjunctive or a disjunctive reading. In the conjunctive reading, a set represents an object of interest and its elements are subparts of the object, forming a composite description. In the disjunctive reading, a set contains mutually exclusive elements and refers to the representation of incomplete knowledge. It does not model an actual object or quantity, but partial information about an underlying object or a precise quantity. This distinction between what we call ontic vs. epistemic sets remains valid for fuzzy sets, whose membership functions, in the disjunctive reading are possibility distributions, over deterministic or random values. This paper examines the impact of this distinction in statistics. We show its importance because there is a risk of misusing basic notions and tools, such as conditioning, distance between sets, variance, regression, etc. when data are set-valued. We discuss several examples where the ontic and epistemic points of view yield different approaches to these concepts.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at International Journal of Approximate Reasoning website : http://www.sciencedirect.com/science/article/pii/S0888613X13001618
HAL Id:hal-01153809
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Universidad de Oviedo (SPAIN)
Laboratory name:
Statistics:download
Deposited By: IRIT IRIT
Deposited On:16 Feb 2015 14:34

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