ISIPTA'07 - FIFTH INTERNATIONAL SYMPOSIUM ON
IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS

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:

Leandro Rego leandro@de.ufpe.br


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