Evolutionary Inference for Functional Data: Using Gaussian Processes on Phylogenies to Study Shape Evolution
Nick S. Jones, John Moriarty · MIMS EPrints (University of Southampton) · 2011
This paper uses the interface between two disciplines�phylogenetics and functional data analysis�to aid the analysis of rich ancestral data like continuous curves. We place Gaus- sian processes on phylogenies in order to perform evolutionary inference on such functional data objects. Unlike morphological summaries, which reduce data dimension, this approach allows one to make inferential statements about curves themselves. We provide a modified covariance function that corrects for the relationships between states at different points on a phylogeny and discuss its use in inference. In general, this covariance is expressed as the solution of an integral equation and we note that, for a given Gaussian process, a set of solutions sufficient for all phylogenies may be precomputed as a library which, for station- ary processes, is one dimensional. This work has relevance for those wanting to perform inference on functional data objects related by an evolutionary process; it also specifies a class of hierarchical clustering algorithms for functional data objects and can be used for multivariate time series forecasting.