Interval straight line fitting

TL;DR

This paper introduces a novel interval hull method for experimental data fitting called 'box slicing algorithm', which guarantees certain solutions without relying on traditional minimization or confidence levels.

Contribution

The paper presents a new constraint satisfaction approach for data fitting that handles uncertainties and outliers without arbitrary weighting or confidence levels.

Findings

Guarantees certain solutions without confidence levels

Handles uncertainties in variables effectively

Applicable to outlier detection and tangent line finding

Abstract

I consider the task of experimental data fitting. Unlike the traditional approach I do not try to minimize any functional based on available experimental information, instead the minimization problem is replaced with constraint satisfaction procedure, which produces the interval hull of solutions of desired type. The method, called 'box slicing algorithm', is described in details. The results obtained this way need not to be labeled with confidence level of any kind, they are simply certain (guaranteed). The method easily handles the case with uncertainties in one or both variables. There is no need for, always more or less arbitrary, weighting the experimental data. The approach is directly applicable to other experimental data processing problems like outliers detection or finding the straight line, which is tangent to the experimental curve.