Abstract

Abstract: Binary trait data record the presence or absence of distinguishing traits in individuals. We treat the problem of estimating ancestral trees with time depth from binary trait data. Each homology class of traits has a unique birth event on the tree, and the birth event of a trait that is visible at the leaves is biased towards the leaves. Traits observed at just one leaf are usually discarded from the data. We model the evolution of sets of traits as a birth-death process for set elements. We integrate many dimensions of the missing data using a Felsenstein-style pruning recursion, and analyse the resulting posterior distribution on trees. We illustrate Bayesian inference for a binary-trait data-set measured on 24 ancient and modern Indo-European languages, extending the model to include rate heterogeneity in the evolution via point-like catastrophe events. The root age and tree topology are of particular interest to the scientists who gathered these data. In our prior on trees, the marginal prior distribution of the root time is uniform. We present an analysis of the robustness of our results to model misspecification, through analysis of predictive distributions for external data, and simulation studies. Part of the work I am presenting is joint with Russell Gray of the University of Auckland, and part is joint with Robin Ryder, of Oxford University.