Simulation-based marginal likelihood for cluster strong lensing
  cosmology
  Comparisons between observed and predicted strong lensing properties of
galaxy clusters have been routinely used to claim either tension or consistency
with $\Lambda$CDM cosmology. However, standard approaches to such cosmological
tests are unable to quantify the preference for one cosmology over another. We
advocate approximating the relevant Bayes factor using a marginal likelihood
that is based on the following summary statistic: the posterior probability
distribution function for the parameters of the scaling relation between
Einstein radii and cluster mass, $\alpha$ and $\beta$. We demonstrate, for the
first time, a method of estimating the marginal likelihood using the X-ray
selected $z>0.5$ MACS clusters as a case in point and employing both N-body and
hydrodynamic simulations of clusters. We investigate the uncertainty in this
estimate and consequential ability to compare competing cosmologies, that
arises from incomplete descriptions of baryonic processes, discrepancies in
cluster selection criteria, redshift distribution, and dynamical state. The
relation between triaxial cluster masses at various overdensities provide a
promising alternative to the strong lensing test.
