  We consider parameter estimation for the spread of the Neolithic incipient
farming across Europe using radiocarbon dates. We model the arrival time of
farming at radiocarbon-dated, early Neolithic sites by a numerical solution to
an advancing wavefront. We allow for (technical) uncertainty in the radiocarbon
data, lack-of-fit of the deterministic model and use a Gaussian process to
smooth spatial deviations from the model. Inference for the parameters in the
wavefront model is complicated by the computational cost required to produce a
single numerical solution. We therefore employ Gaussian process emulators for
the arrival time of the advancing wavefront at each radiocarbon-dated site. We
validate our model using predictive simulations.
