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FOURTH
INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

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Carnegie Mellon University

Pittsburgh, PA, USA

July 20-23 2005

#
ISIPTA'05 ELECTRONIC PROCEEDINGS

## Alberto Piatti, Marco Zaffalon, Fabio Trojani

# Limits of Learning from Imperfect Observations under Prior Ignorance: the Case of the Imprecise Dirichlet Model

### Abstract

Consider a relaxed multinomial setup, in which there may be mistakes
in observing the outcomes of the process--this is often the case in
real applications. What can we say about the next outcome if we
start learning about the process in conditions of prior ignorance?
To answer this question we extend the imprecise Dirichlet model to
the case of imperfect observations and we focus on posterior
predictive probabilities for the next outcome. The results are very
surprising: the posterior predictive probabilities are vacuous,
irrespectively of the amount of observations we do, and however
small is the probability of doing mistakes. In other words, the
imprecise Dirichlet model cannot help us to learn from data when the
observational mechanism is imperfect. This result seems to rise a
serious question about the use of the imprecise Dirichlet model for
practical applications, and, more generally, about the possibility
to learn from imperfect observations under prior ignorance.

** Keywords. ** Predictive Bayesian Inference, Imprecise Dirichlet Model, Vacuous Predictive Probabilities, Imperfect Observational Mechanism

** Paper Download **

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** Authors addresses: **

Alberto Piatti

Salita S.Michele 2

6500 Bellinzona

Marco Zaffalon

Galleria 2

CH-6928 Manno

Switzerland

Fabio Trojani

Rosenbergstr. 52

CH-9000 St.Gallen

** E-mail addresses: **

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