Interval straight line fitting
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2001
 arXiv:
 arXiv:math/0108163
 Bibcode:
 2001math......8163G
 Keywords:

 Mathematics  Numerical Analysis;
 Mathematics  Optimization and Control;
 Physics  Data Analysis;
 Statistics and Probability;
 65G40;
 65Z05
 EPrint:
 21 pages, LaTEX2e, 4 figures, submitted to Reliable Computing