Evolutionary inference for functional data: using Gaussian processes on phylogenies of functional data objects.
MSc(R) thesis, University of Glasgow.
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This thesis explores the use of phylogenetics and functional data analysis for the analysis of continuous ancestral data such as continuous curves. Gaussian processes (GPs) are placed on phylogenies in order to perform evolutionary inferences on the functional data objects. The mean and covariance functions of the GP model the relationships between different states on the phylogeny.
The functional data objects are completely described by the spatial and temporal parameters within the covariance functions, allowing inferences to be made, for example, by the method of maximum likelihood estimation. Inferences
are successfully made on known phylogenies, phylogenies with missing ancestral data and on phylogenies of unknown topology. This work is potentially useful for those wanting to compute evolutionary inferences on continuous ancestral data, for which phylogenetic GPs are shown to be an
efficient and promising tool.
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