Bestimmung von Messunsicherheiten mittels Bootstrapping in der Formanalyse

Abstract

The methods of the Guide to the Expression of Uncertainty in Measurement, e.g. Law of propagation of uncertainty or Monte-Carlo simulations, are the most applied guidelines in the framework of measurement sciences. These methods require a-priori knowledge of the statistical distribution of the taken sample. However, in some practical cases, this condition cannot be fulfilled. In descriptive statistics, analysis methods are known that do not required knowledge of the underlying distribution of the data. One well-known algorithm is the bootstrapping. In this contribution, the bootstrap algorithm is applied to the surface analysis to derive confidence intervals of estimated parameters, exemplified by the adjustment of an elliptic ring-focus paraboloid. Introducing kernel density estimation, the unknown probability density functions of the estimates are approximated and transformed to the resulting focal area to derive the level of confidence of the intervals.