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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 **

## Jeff Paris, P.N.Watton, and George Wilmers

# On the Distribution of Natural Probability Functions

** Abstract **

The purpose of this note is to describe the underlying insights and
results obtained by the authors, and others, in a series of papers
aimed at modelling the distribution of `natural' probability
functions, more precisely the probability functions on $\{0,1\}$
which we encounter naturally in the real world as subjects for
statistical inference, by identifying such functions with large,
random, sentences of the propositional calculus. We explain how this
approach produces a robust parameterised family of priors, $J_n$,
with several of the properties we might have hoped for in the context,
for example marginalisation, invariance under (weak) renaming, and
an emphasis on multivariate probability functions exhibiting high
interdependence between features.

** Keywords. ** Prior probability, imprecise probability, random sentences, probabilistic reasoning, uncertain reasoning.

The paper is available in the following formats:

** Authors addresses: **

Department of Mathematics,

Manchester University,

Manchester,

M13 9PL,

UK.

** E-mail addresses: **

** Related Web Sites **

Jeff Paris

George Wilmers

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