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The 70-month Swift/BAT catalogue provides a sensitive view of theextragalactic X-ray sky at hard energies (>10 keV) containing about 800 ActiveGalactic Nuclei. We explore its content in heavily obscured, Compton-thick AGNby combining the BAT (14-195 keV) with the lower energy XRT (0.3-10 keV) data.We apply a Bayesian methodology using Markov chains to estimate the exactprobability distribution of the column density for each source. We find 53possible Compton-thick sources (with probability 3 to 100%) translating to a~7% fraction of the AGN in our sample. We derive the first parametricluminosity function of Compton-thick AGN. The unabsorbed luminosity functioncan be represented by a double power-law with a break at $L_{\star} 2 \times10^{42}$ $\rm ergs~s^{-1}$ in the 20-40 keV band.

Compton Thick AGN in the 70 Month Swift-BAT All-Sky Hard X-ray Survey: a Bayesian approach