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ISIPTA'09 -
SIXTH INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS

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Durham University, Department of Mathematical Sciences

Durham, United Kingdom

Tuesday 14 to Saturday 18 July 2009

## ELECTRONIC PROCEEDINGS

## Thomas Fetz

# Multivariate Models and Confidence Intervals: A Local Random Set Approach

### Abstract

This article is devoted to the propagation of families of confidence
intervals obtained by non-parametric methods through multivariate
functions comprising the semantics of confidence limits. At fixed
confidence level, local random sets are defined whose aggregation admits
the calculation of upper probabilities of events. In the multivariate
case, a number of ways of combinations is highlighted to encompass
independence and unknown interaction using random set independence and
Fr\'echet bounds. For all cases we derive formulas for the corresponding
upper probabilities and elaborate how they relate. The methods are
exemplified by means of an example from structural mechanics.

** Keywords. ** Confidence intervals, non-parametric models of uncertainty, random sets, fuzzy sets, upper probability, independence, unknown interaction, Fr\'echet bounds

** Paper Download **

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** Authors addresses: **

Institut für Grundlagen der Bauingenieurwissenschaften, AB Technische Mathematik,

Technikerstraße 13, Innsbruck

** E-mail addresses: **

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