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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

## Leandro Rego

# Conditioning in Chaotic Probabilities Interpreted as a Generalized Markov Chain

### Abstract

We propose a new definition for conditioning in the Chaotic
Probability framework. We show that the Conditional Chaotic Probability model that we propose can be given the interpretation of a generalized Markov chain. Chaotic Probabilities were introduced by Fine et al. as an attempt to model chance phenomena with a usual set of measures ${\cal M}$ endowed with an {\em objective, frequentist interpretation} instead of a compound hypothesis or behavioral subjective one. We follow the presentation of the univariate case chaotic probability model and provide an instrumental interpretation of random process measures consistent with a conditional chaotic probability source, which can be used as a tool for simulation of our model. Given a finite time series, we also present a universal method for estimation of conditional chaotic probability models that is based on the analysis of the relative frequencies taken along a set of subsequences chosen by a given set of rules.

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

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** Authors addresses: **

Rua Muniz Tavares 25, apt. 902 - Jaqueira

Recife-PE Brazil

CEP:52050-170

** E-mail addresses: **

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