ISIPTA'07 - FIFTH INTERNATIONAL SYMPOSIUM ON
IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS

Charles University, Faculty of Mathematicsand Physics
Prague, Czech Republic
16-19 July 2007

ELECTRONIC PROCEEDINGS

Thierry Denoeux, Astride Aregui

Constructing Predictive Belief Functions from Continuous Sample Data Using Confidence Bands

Abstract

We consider the problem of quantifying our belief in future values of a random variable X with unknown distribution P_X, based on the observation of a random sample from the same distribution. The adopted uncertainty representation framework is the Transferable Belief Model, a subjectivist interpretation of belief function theory. In a previous paper, the concept of predictive belief function at a given confidence level was introduced, and it was shown how to build such a function when X is discrete. This work is extended here to the case where X is a continuous random variable, based on step or continuous confidence bands.

Keywords. Dempster-Shafer Theory, Evidence Theory, Transferable Belief Model, p-box, distribution band

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Authors addresses:

Thierry Denoeux
U.M.R. C.N.R.S. 6599 Heudiasyc,
Centre de Recherches de Royallieu
B.P. 20529
F-60205 Compi├Ęgne Cedex
France

Astride Aregui
Universite de Technologie de Compiegne
Universite de Technologie de Compiegne
Heudiasyc
Centre de Recherches de Royallieu
B.P. 20529
F-60205 Compiegne Cedex

E-mail addresses:

Thierry Denoeux tdenoeux@hds.utc.fr
Astride Aregui aaregui@hds.utc.fr

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