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：我们提出了对历史语言学中最初发展的“波模型”的数学形式化，并将其进一步应用于人类科学领域。该模型假设新特征在种群中出现，并根据种群间的接近程度向邻近种群扩散。它主要用于描述密切关联种群（例如多种方言）的共同演化。这种持续接触的情况无法通过基于树结构的竞争模型准确呈现。我们构建了一个完全贝叶斯生成模型，其中创新沿着固定图传播，并根据死亡过程消失。随后，我们开发了一种在吉布斯采样器内嵌套梅特罗波利斯-黑斯廷斯算法的方法，用于对图的后验分布进行采样。我们在模拟数据集以及多个真实数据集上验证了该方法。