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A hierarchical Bayesian method is applied to the analysis of Type-Iasupernovae (SNIa) observations to constrain the properties of the dark matterhaloes of galaxies along the SNIa lines-of-sight via their gravitationallensing effect. The full joint posterior distribution of the dark matter haloparameters is explored using the nested sampling algorithm {\sc MultiNest},which also efficiently calculates the Bayesian evidence, thereby facilitatingrobust model comparison. We first demonstrate the capabilities of the method byapplying it to realistic simulated SNIa data, based on the real 3-year datarelease from the Supernova Legacy Survey (SNLS3). Assuming typical values forthe halo parameters in our simulations, we find that a catalogue analogous tothe existing SNLS3 data set is incapable of detecting the lensing signal, but acatalogue containing approximately three times as many SNIa does produce robustand accurate parameter constraints and model selection results for two halomodels: a truncated singular isothermal sphere (SIS) and aNavarro--Frenk--White (NFW) profile, thereby validating our analysismethodology. In the analysis of the real SNLS3 data, contrary to previousstudies, we obtain only a very marginal detection of a lensing signal and weakconstraints on the halo parameters for the truncated SIS model, although theseconstraints are tighter than those obtained from the equivalent simulated SNIadata set. This difference is driven by a preferred value of $\eta \approx 1$ inthe assumed scaling-law $\sigma \propto L^\eta$ between velocity dispersion andluminosity, which is somewhat higher than the canonical values of $\eta =\tfrac{1}{4}$ and $\eta = \tfrac{1}{3}$ for early and late-type galaxies,respectively, and leads to a stronger lensing effect by the halo. No detectionof a lensing signal is made for the NFW model.

Bayesian constraints on dark matter halo properties using gravitationally-lensed supernovae