I was told the Wave model in linguistics had not been formalised. Here is an attempt at it. Note that many things remain to be done, check the discussion for that.
The method/model I propose, WaST, can be used on any cognacy dataset. I'll put the code on git soon.
arxiv.org/abs/2604.08220
We propose a mathematical formalisation of the ``wave model'' originally developed in historical linguistics but with further applications in human sciences. This model assumes new traits appear in a population and spread to nearby populations depending on their closeness. It is mostly used to describe joint evolution of closely related populations, for example of several dialects. These situations of permanent contact are not accurately represented by its competitors based on tree structures. We built a fully Bayesian generative model where innovation spread along a fixed graph and disappear according to a death process. We then develop a Metropolis-Hastings within Gibbs sampler to sample from the posterior distribution on the graph. We test our method on simulated datasets as well as on several real dataset.
