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.

翻译：本文对最初在历史语言学中发展、但进一步应用于人文科学的“波模型”进行了数学形式化。该模型假设新特征在群体中出现，并根据邻近程度扩散至周边群体，主要用于描述密切关联群体（例如若干方言）的联合演化。这种持续接触的情境无法被基于树结构的竞争模型准确刻画。我们构建了一个完全贝叶斯生成模型，其中创新沿固定图结构传播，并根据消亡过程消失。随后，我们开发了一种在吉布斯采样器内嵌的Metropolis-Hastings算法，用于从图结构后验分布中采样。该方法在模拟数据集及多个真实数据集上均进行了测试。