  Orbit superposition models are a non-parametric dynamical modelling technique
to determine the mass of a galaxy's central supermassive black hole (SMBH), its
stars, or its dark-matter halo. One of the main problems is how to decide which
model out of a large pool of trial models based on different assumed mass
distributions represents the true structure of an observed galaxy best. We show
that the traditional approach to judge models solely by their goodness-of-fit
can lead to substantial biases in estimated galaxy properties caused by varying
model flexibilities. We demonstrate how the flexibility of the models can be
estimated using bootstrap iterations and present a model selection framework
that removes these biases by taking the variable flexibility into account in
the model evaluation. We extend the model selection approach to optimize the
degree of regularisation directly from the data. Altogether, this leads to a
significant improvement of the constraining power of the modeling technique. We
show with simulations that one can reconstruct the mass, anisotropy and viewing
angle of an axisymmetric galaxy with a few percent accuracy from realistic
observational data with fully resolved line-of-sight velocity distributions
(LOSVDs). In a first application, we reproduce a photometric estimate of the
inclination of the disk galaxy NGC 3368 to within 5 degree accuracy from
kinematic data that cover only a few sphere-of-influence radii around the
galaxy's SMBH. This demonstrates the constraining power that can be achieved
with orbit models based on fully resolved LOSVDs and a model selection
framework.
