We present a novel method for co-registration of two independent statistical shape models. We solve the problem of aligning a face model to a skull model with stochastic optimization based on Markov Chain Monte Carlo (MCMC). We create a probabilistic joint face-skull model and show how to obtain a distribution of plausible face shapes given a skull shape. Due to environmental and genetic factors, there exists a distribution of possible face shapes arising from the same skull. We pose facial reconstruction as a conditional distribution of plausible face shapes given a skull shape. Because it is very difficult to obtain the distribution directly from MRI or CT data, we create a dataset of artificial face-skull pairs. To do this, we propose to combine three data sources of independent origin to model the joint face-skull distribution: a face shape model, a skull shape model and tissue depth marker information. For a given skull, we compute the posterior distribution of faces matching the tissue depth distribution with Metropolis-Hastings. We estimate the joint face-skull distribution from samples of the posterior. To find faces matching to an unknown skull, we estimate the probability of the face under the joint faceskull model. To our knowledge, we are the first to provide a whole distribution of plausible faces arising from a skull instead of only a single reconstruction. We show how the face-skull model can be used to rank a face dataset and on average successfully identify the correct match in top 30%. The face ranking even works when obtaining the face shapes from 2D images. We furthermore show how the faceskull model can be useful to estimate the skull position in an MR-image.