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

TL;DR

This paper explores how interval analysis can be applied to experimental data fitting, providing rigorous interval results or probabilistic summaries like means and standard deviations, bridging interval methods with traditional statistical approaches.

Contribution

It demonstrates how to process experimental data using interval analysis and convert results into familiar statistical summaries, enhancing the reliability and interpretability of data fitting.

Findings

Interval methods can produce guaranteed, rigorous results.

Results can be expressed as means and standard deviations.

The approach bridges interval analysis with statistical data analysis.

Abstract

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.