WaST: a formalisation of the Wave model with associated statistical inference and applications

TL;DR

This paper formalizes the wave model from historical linguistics using Bayesian methods, enabling better analysis of trait spread among populations with complex contact patterns.

Contribution

It introduces a Bayesian generative model and inference algorithm for the wave model, extending its applicability to populations with ongoing contact.

Findings

Successfully tested on simulated datasets

Applied to real linguistic data

Demonstrated improved modeling of trait spread

Abstract

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.