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SECOND INTERNATIONAL
SYMPOSIUM ON

IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

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Cornell University

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Ithaca, NY, USA

26 - 29 June 2001

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ELECTRONIC PROCEEDINGS

## Nic Wilson

# Modified upper and lower probabilities based on imprecise likelihoods

### Abstract

The large sample behaviour is examined for upper and lower
probabilities generated by precise priors (on a finite set) and
imprecise likelihoods, for equally independently distributed
variables taking values in a finite set. It can easily happen that
the posterior upper probability of $\theta$ will tend to $1$ in
situations where the relative frequencies are tending to a measure
far removed from the set of conditional measures associated with
$\theta$. A number of different modifications to upper and lower probability
are made in such a way that the posterior probabilities will, with
probability one, become or tend to $0$ in such situations; these all
involve rejecting measures which are extremely implausible given the
data, and hence considering more restricted sets of likelihoods.

** Keywords. ** Upper and lower probability, imprecise likelihoods, large sample behaviour, Bernouilli trials

** Format. **Postscript

**Paper Download **

The paper is availabe in the following sites:

** Authors addresses: **

School of Computing and Mathematical Sciences

Oxford Brookes University

Gipsy Lane

Headington

Oxon,

UK

OX3 0BP

** E-mail addresses: **

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