2008-02-neumann

From CS Colloquium

In many engineering disciplines the interesting model parameters are estimated from a large number of heterogeneous and redundant observations by a least-squares adjustment. The significance of the model parameters and the model selection itself are checked with statistical hypothesis tests. In case of observations, this strategy is straight forward: After formulating a null hypothesis, the test decision is based on the comparison of a crisp test value with a quantile value. The acceptance and the rejection of the null hypothesis are strongly related with two types of errors. A type I error occurs if the null hypothesis is rejected, although it is true. A type II error occurs if the null hypothesis is accepted, although it is false. This procedure is well known in case of exact values for the observations.

If the uncertainty budget of the observations is assumed to comprise interval errors or fuzzy uncertainty, the classical test strategies have to be extended accordingly. In this study, we focus on one- and multidimensional hypothesis tests in case of interval errors for the observations and fuzzy regions for a type I error. The applied procedure is outlined in detail showing both theory and numerical examples in geodetic applications.