Congruence analysis of geodetic networks – hypothesis tests versus model selection by information criteria

Geodetic deformation analysis can be interpreted as a model selection problem. The null model indicates that no deformation has occurred. It is opposed to a number of alternative models, which stipulate different deformation patterns. A common way to select the right model is the usage of a statistical hypothesis test. However, since we have to test a series of deformation patterns, this must be a multiple test. As an alternative solution for the test problem, we propose the -value approach. Another approach arises from information theory. Here, the Akaike information criterion (AIC) or some alternative is used to select an appropriate model for a given set of observations. Both approaches are discussed and applied to two test scenarios: A synthetic levelling network and the Delft test data set. It is demonstrated that they work but behave differently, sometimes even producing different results. Hypothesis tests are well-established in geodesy, but may suffer from an unfavourable choice of the decision error rates. The multiple test also suffers from statistical dependencies between the test statistics, which are neglected. Both problems are overcome by applying information criterions like AIC.

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