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FIRST INTERNATIONAL
SYMPOSIUM ON

IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

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Ghent, Belgium

30 June - 2 July 1999

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** ELECTRONIC PROCEEDINGS **

## Peter Walley

# Towards a Unified Theory of Imprecise Probability

** Abstract **

Belief functions, possibility measures and Choquet capacities
of order 2, which are special kinds of coherent upper or lower
probability, are amongst the most popular mathematical models
for uncertainty and partial ignorance. I give examples to show
that these models are not sufficiently general to represent some
common types of uncertainty. Coherent lower previsions and sets
of probability measures are considerably more general but they
may not be sufficiently informative for some purposes.
I discuss two other models for uncertainty, involving sets of
desirable gambles and partial preference orderings. These are
more informative and more general than the previous models, and
they may provide a suitable mathematical setting for a unified
theory of imprecise probability.

** Keywords. ** Choquet capacity, coherence, comparative probability, desirable gambles, imprecise probability, incomplete preference, lower prevision, lower probability.

The paper is available in the following formats:

** Authors addresses: **

36 Bloomfield Terrace

Lower Hutt

New Zealand

** E-mail addresses: **

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