Breakthrough in Interval Data Fitting II. From Ranges to Means and Standard Deviations

Details Breakthrough in Interval Data Fitting II. From Ranges to Means and Standard Deviations Breakthrough in Interval Data Fitting II. From Ranges to Means and Standard Deviations

2009-03-02

arxiv.org/abs/0903.0365v1

Physics

Data Analysis, Statistics and Probability

No figures, submitted to XII Conference on Evolutionary Algorithms and Global Optimization (XII KAEiOG), to be held on June 1-

Scientific paper

Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all. Worse yet, if this happens, then we are left in the state of complete ignorance concerning the unknown parameters of interest. This is in sharp contrast with widespread statistical methods of data analysis. In this paper I show the connections between those two approaches: how to process experimental data rigorously, using interval methods, and present the final results either as intervals (guaranteed, rigorous results) or in a more familiar probabilistic form: as a mean value and its standard deviation.

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