Bayesian approach to gravitational lens model selection: constraining H_0 with a selected sample of strong lenses

TL;DR

This paper develops a Bayesian model selection method for strong gravitational lens systems to accurately estimate the Hubble constant, demonstrating its effectiveness on simulated and real data with potential for future large surveys.

Contribution

It introduces a Bayesian framework for selecting homogeneous lens subsamples suitable for cosmological inference, improving H_0 estimation accuracy from gravitational lens data.

Findings

Bayes factor analysis effectively identifies simple power-law lens models.

The method recovers the Hubble constant within 3σ uncertainty on synthetic data.

Application to real lens systems yields H_0=76+15-5 km/s/Mpc.

Abstract

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