Bayesian approach to gravitational lens model selection: constraining H0 with a selected sample of strong lenses

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 catalogue 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 3σ 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 favours a simple power-law model description with high statistical significance. Assuming a flat Λ cold dark matter cosmology, the combined likelihood data analysis of such systems gives the Hubble constant H₀ = 76^{+ 15}_{- 5} km s^{- 1} Mpc^{- 1} 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 data sets and the method described here can be particularly useful to select homogeneous lens subsamples adapted to perform unbiased cosmological parameter inference.