###
3rd International Symposium
on

Imprecise
Probabilities and Their Applications

ISIPTA '03

#####
University of Lugano

Lugano, Switzerland

14-17 July 2003

####
ELECTRONIC PROCEEDINGS

# On the symbiosis of two concepts of conditional interval probability

### Abstract

This paper argues in favor of the thesis that two different
concepts of conditional interval probability are needed, in order
to serve the huge variety of tasks conditional probability has in
the classical setting of precise probabilities. We compare the
commonly used intuitive concept of conditional interval
probability with the canonical concept, and see, in particular,
that the canonical concept is the appropriate one to generalize
the idea of transition kernels to interval probability: only the
canonical concept allows reconstruction of the original interval
probability from the marginals and conditionals, as well as the
powerful formulation of Bayes Theorem.

** Keywords. ** Conditional interval probability, intuitive concept of conditional interval probability, canonical concept of conditional interval probability, conditioning, updating, Theorem of Total Probability, Markov chains, Bayes' Theorem, decision theory

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** Authors addresses: **

Kurt Weichselberger

Dep. of Statistics

Ludwigstr. 33

D 80539 Muenchen

Thomas Augustin

Ludwigstr. 33

D-80539 Munich

Germany

** E-mail addresses: **

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