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tokens: ( 2013 , 2014 ), and further details on the strong lensing modeling of MACSJ1149.5+2223 are provided in a dedicated paper (Grillo et al. 2015a ). 4.2.1. Definition of the Mass Model Different mass models have been explored for this galaxy cluster, but only the best-fitting one is discussed here. The projected dimensionless total surface mass density of 300 cluster members within the WFC3 field of view of the CLASH observations is modeled as a dual pseudoisothermal elliptical mass distribution (dPIE; Elíasdóttir et al. 2007 ) with vanishing ellipticity and core radius. The zero-core dPIE profile corresponds to the three-dimensional mass density profile:The galaxy luminosity values in the F160W band are used to assign the relative weights to their total mass profile. The galaxy total M / L ratio is scaled with luminosity as , thus mimicking the so-called “tilt” of the Fundamental Plane. The values of axis ratio, PA, effective velocity dispersion, and truncation radius of the two cluster members closest in projection to the central and southern images of the SN Refsdal host are left free. To complete the total mass distribution of the galaxy cluster, three additional mass components are added to describe the cluster dark matter halo on physical scales larger than those typical of the individual cluster members. These cluster halo components are parametrized as two-dimensional pseudo-isothermal elliptical mass profiles (PIEMD as defined by Kassiola Kovner 1993 ; see also Grillo et al. 2015a ). No external shear or higher-order perturbations are included in the model. The number of free parameters associated with the model of the cluster total mass distribution is 28. 4.2.2. Definition of the Inputs The positions of the multiple images belonging to the 10 systems of the gold sample and to 18 knots of the SN Refsdal host are the observables over which the values of the model parameters are optimized. The adopted positional uncertainty of each image is 0065. The redshift values of the 7 spectroscopically confirmed gold systems are fixed, while the remaining 3 systems are included with a uniform prior on the value of , where D ds and D s are the deflector-source and observer-source angular diameter distances, respectively. In total, 88 observed image positions are used to reconstruct the cluster total mass distribution. 4.2.3. Description of the Inference Process and Error Estimation The best-fitting, minimum- model is obtained by minimizing the distance between the observed and model-predicted positions of the multiple images in the lens plane. A minimum value of 1441, corresponding to an rms offset between the image observed and reconstructed positions of 026, is found. To sample the posterior probability distribution function of the model parameters, the image positional uncertainty is increased until the value of the is comparable to the number of the degrees of freedom (89), and standard Markov chain Monte Carlo (MCMC) methods are used. The