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The Extragalactic Background Light (EBL) is the main radiation fieldresponsible for attenuating extragalactic gamma-ray emission at very highenergies, but its precise spectral intensity is not fully determined.Therefore, disentangling propagation effects from the intrinsic spectralproperties of gamma-ray sources (such as active galactic nuclei, AGN) is theprimary challenge to interpreting observations of these objects. We present aBayesian and Markov Chain Monte Carlo approach to simultaneously inferparameters characterizing the EBL and the intrinsic spectra in a combined fitof a set of sources, which has the advantage of easily incorporating theuncertainties of both sets of parameters into one another throughmarginalization of the posterior distribution. Taking a sample of syntheticblazars observed by the ideal CTA configuration, we study the effects on theEBL constraints of combining multiple observations and varying their exposure.We also apply the methodology to a set of 65 gamma-ray spectra of 36 differentAGNs measured by current Imaging Atmospheric Cherenkov Telescopes, usingHamiltonian Monte Carlo as a solution to the difficult task of sampling inspaces with a high number of parameters. We find robust constraints in themid-IR region while simultaneously obtaining intrinsic spectral parameters forall of these objects. In particular, we identify Markarian 501 (Mkn 501) flaredata (HEGRA/1997) as essential for constraining the EBL above 30$\mu$m.

Simultaneously unveiling the EBL and intrinsic spectral parameters of gamma-ray sources with Hamiltonian Monte Carlo