Physics – Data Analysis – Statistics and Probability
Scientific paper
2009-03-02
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
This is the first of two papers describing the process of fitting experimental data under interval uncertainty. Here I present the methodology, designed from the very beginning as an interval-oriented tool, meant to replace to the large extent the famous Least Squares (LSQ) and other slightly less popular methods. Contrary to its classical counterparts, the presented method does not require any poorly justified prior assumptions, like smallness of experimental uncertainties or their normal (Gaussian) distribution. Using interval approach, we are able to fit rigorously and reliably not only the simple functional dependencies, with no extra effort when both variables are uncertain, but also the cases when the constitutive equation exists in implicit rather than explicit functional form. The magic word and a key to success of interval approach appears the Hausdorff distance.
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