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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

## Leandro Rego, Terrence Fine

# Estimation of Chaotic Probabilities

### Abstract

A Chaotic Probability model is a usual set of probability
measures, ${\cal M}$, the totality of which is endowed with an
{\em objective, frequentist interpretation} as opposed to being
viewed as a statistical compound hypothesis or an imprecise
behavioral subjective one. In the prior work of Fierens and Fine,
given finite time series data, the estimation of the Chaotic
Probability model is based on the analysis of a set of relative
frequencies of events taken along a set of subsequences selected
by a set of rules. Fierens and Fine proved the existence of
families of causal subsequence selection rules that can make
${\cal M}$ visible, but they did not provide a methodology for
finding such family. This paper provides a universal methodology
for finding a family of subsequences that can make ${\cal M}$
visible such that relative frequencies taken along such
subsequences are provably close enough to a measure in ${\cal M}$
with high probability.

** Keywords. ** Imprecise Probabilities, Foundations of Probability, Church Place Selection Rules, Probabilistic Reasoning, Complexity.

** Paper Download **

The paper is availabe in the following formats:

** Authors addresses: **

Leandro Rego

706 E. Seneca st. #2

Ithaca - NY - USA

Zip Code: 14850

Terrence Fine

School of ECE

1391 Ellis Hollow Rd

Cornell University

Ithaca, NY 14850, USA

** E-mail addresses: **

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