  The 70-month Swift/BAT catalogue provides a sensitive view of the
extragalactic X-ray sky at hard energies (>10 keV) containing about 800 Active
Galactic Nuclei. We explore its content in heavily obscured, Compton-thick AGN
by 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 exact
probability distribution of the column density for each source. We find 53
possible Compton-thick sources (with probability 3 to 100%) translating to a
~7% fraction of the AGN in our sample. We derive the first parametric
luminosity function of Compton-thick AGN. The unabsorbed luminosity function
can be represented by a double power-law with a break at $L_{\star} 2 \times
10^{42}$ $\rm ergs~s^{-1}$ in the 20-40 keV band.
