Abstract Bayesian phylogenetic methods provide a set of tools to efficiently evaluate large linguistic datasets by reconstructing phylogenies—family trees—that represent the history of language families. These methods provide a powerful way to test hypotheses about prehistory, regarding the subgrouping, origins, expansion, and timing of the languages and their speakers. Through phylogenetics, we gain insights into the process of language evolution in general and into how fast individual features change in particular. This article introduces Bayesian phylogenetics as applied to languages. We describe substitution models for cognate evolution, molecular clock models for the evolutionary rate along the branches of a tree, and tree generating processes suitable for linguistic data. We explain how to find the best-suited model using path sampling or nested sampling. The theoretical background of these models is supplemented by a practical tutorial describing how to set up a Bayesian phylogenetic analysis using the software tool BEAST2.
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