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ISIPTA'07 -
FIFTH INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS

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Charles University, Faculty of Mathematicsand Physics

Prague, Czech Republic

16-19 July 2007

## ELECTRONIC PROCEEDINGS

## Robert Hable

# Data-Based Decisions under Imprecise Probability and Least Favorable Models

### Abstract

Data-based decision theory under imprecise probability has to deal
with optimisation problems where direct solutions are often
computationally intractable. Using the $\Gamma$-minimax optimality
criterion, the computational effort may significantly be reduced in
the presence of a least favorable model. In 1984, A. Buja derived a
neccessary and sufficient condition for the existence of a least
favorable model in a special case. The present article proofs that
essentially the same result is valid in case of general coherent
upper expectations. This is done mainly by topological arguments in
combination with some of L. Le Cam's decision theoretic concepts. It
is shown how least favorable models could be used to deal with
situations where the distribution of the data as well as the prior
is assumed to be imprecise.

** Keywords. ** Decision theory, robust statistics, imprecise probability, coherent upper expectations, Le Cam, equivalence of models, least favorable models

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** Authors addresses: **

Department of Statistics

LMU Munich

Ludwigstr. 33

D-80539 Munich

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