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C. Harmening, H.-B. Neuner:
"Using model selection criteria to determine the optimal number of B-spline control points for areal deformation modelling";
Talk: Joint International Symposium on Deformation Monitoring 2016, Wien; 2016-03-30 - 2016-04-01; in: "Proceedings of Joint International Symposium on Deformation Monitoring 2016", (2016), Paper ID 44, 9 pages.

The increased use of areal measurement techniques in engineering geodesy requires the development of adequate areal analysis strategies. In this paper, an outline of a research project is presented which aims to develop a spatiotemporal continuous collocation in order to describe areal deformations.
The trend component of the collocation is modelled by estimated B-spline surfaces in this study. Among other form parameters B-spline surfaces are characterized by the number of estimated control points. Typically, the appropriate number of control points is set under consideration of parsimony by trial-and-error procedures. In this contribution the determination of the number of control points is regarded as a model selection problem. Two linear model selection criteria - the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) - are investigated: Although both criteria lead to a penalized maximum likelihood estimation, they are based on different principles: The AIC is an information-theoretic approach, which approximates the Kullback-Leibler distance, whereas the BIC is based on Bayes´ theorem and approximates the marginal density of the respective likelihood. Both criteria are applied to simulated data sets and the results are analyzed, compared and evaluated. Based on the theoretical backgrounds as well as on the empirical evaluation, the criteria´s usage is justified. Furthermore, nonlinear methods from the field of statistical learning theory are investigated.

AIC, BIC, B-spline surfaces, deformation modelling, model selection, VC dimension