  We consider a wavefront model for the spread of Neolithic culture across
Europe, and use Bayesian inference techniques to provide estimates for the
parameters within this model, as constrained by radiocarbon data from Southern
and Western Europe. Our wavefront model allows for both an isotropic background
spread (incorporating the effects of local geography), and a localized
anisotropic spread associated with major waterways. We introduce an innovative
numerical scheme to track the wavefront, and use Gaussian process emulators to
further increase the efficiency of our model, thereby making Markov chain Monte
Carlo methods practical. We allow for uncertainty in the fit of our model, and
discuss the inferred distribution of the parameter specifying this uncertainty,
along with the distributions of the parameters of our wavefront model. We
subsequently use predictive distributions, taking account of parameter
uncertainty, to identify radiocarbon sites which do not agree well with our
model. These sites may warrant further archaeological study, or motivate
refinements to the model.
