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.
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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:
| Leandro Rego | lcr26@cornell.edu |
| Terrence Fine | tlfine@ece.cornell.edu |