  Bayesian model selection methods provide a self-consistent probabilistic
framework to test the validity of competing scenarios given a set of data. We
present a case study application to strong gravitational lens parametric
models. Our goal is to select a homogeneous lens subsample suitable for
cosmological parameter inference. To this end we apply a Bayes factor analysis
to a synthetic catalog of 500 lenses with power-law potential and external
shear. For simplicity we focus on double-image lenses (the largest fraction of
lens in the simulated sample) and select a subsample for which astrometry and
time-delays provide strong evidence for a simple power-law model description.
Through a likelihood analysis we recover the input value of the Hubble constant
to within 3\sigma statistical uncertainty. We apply this methodology to a
sample of double image lensed quasars. In the case of B1600+434, SBS 1520+530
and SDSS J1650+4251 the Bayes' factor analysis favors a simple power-law model
description with high statistical significance. Assuming a flat \LambdaCDM
cosmology, the combined likelihood data analysis of such systems gives the
Hubble constant H_0=76+15-5 km/s/Mpc having marginalized over the lens model
parameters, the cosmic matter density and consistently propagated the
observational errors on the angular position of the images. The next generation
of cosmic structure surveys will provide larger lens datasets and the method
described here can be particularly useful to select homogeneous lens subsamples
adapted to perform unbiased cosmological parameter inference
