title: Evolutionary inference for function-valued traits: Gaussian process regression on phylogenies.
abstract: Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated owing to phylogenetic relationships. In this paper, we give a flexible statistical model for such data, by combining assumptions from phylogenetics with Gaussian processes. We describe its use as a non-parametric Bayesian prior distribution, both for prediction (placing posterior distributions on ancestral functions) and model selection (comparing rates of evolution across a phylogeny, or identifying the most likely phylogenies consistent with the observed data). Our work is integrative, extending the popular phylogenetic Brownian motion and Ornstein-Uhlenbeck models to functional data and Bayesian inference, and extending Gaussian process regression to phylogenies. We provide a brief illustration of the application of our method.
authors.affiliation: Department of Mathematics, Imperial College London, London, UK.
authors.forename: Nick S
authors.initials: NS
authors.lastname: Jones
authors.forename: John
authors.initials: J
authors.lastname: Moriarty
mesh_terms: D008954:Models, Biological; D010802:Phylogeny