Bayesian inference for a wavefront model of the Neolithisation of Europe

Details Bayesian inference for a wavefront model of the Neolithisation of Europe Bayesian inference for a wavefront model of the Neolithisation of Europe

2012-03-20

arxiv.org/abs/1203.4471v1

Physics

Biological Physics

15 pages, 11 figures

Scientific paper

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, allowing us to simulate the times of the first arrival at any site orders of magnitude more efficiently than traditional PDE approaches. We adopt a Bayesian approach to inference and use Gaussian process emulators to facilitate further increases in efficiency in the inference scheme, thereby making Markov chain Monte Carlo methods practical. We allow for uncertainty in the fit of our model, and also infer a parameter specifying the magnitude of this uncertainty. We obtain a magnitude for the background spread of order 1 km/year, which is consistent with previous studies. The additional anisotropic spread along the Danube and Rhine rivers is of order 1 km/year; the enhanced spread along coastlines, considered for the region as a whole, is less significant, of order 0.3 km/year. The uncertainty within the model is of order 600 years; this quantifies the timescale on which the observed spread across Europe can accurately be modeled as a simple expanding wavefront as considered here. We subsequently use predictive distributions, which take 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.

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