What is an efficient way to project functional data to a lower dimensional subspace? IPCA.R

Assuming a real-valued trait is measured across the tips/leaves of a phylogeny, and given a Gaussian Process prior distribution for its values through the phylogeny,

1. how can one infer its posterior distribution at internal nodes of the phylogeny? ANR.R
2. how can one infer the hyperparameters of the prior distribution? HPE.R (you'll also need this file with additional functions HPE_functions.R )

The necessary background to this code is provided in the report paper "Ancestral Inference from Functional Data: Statistical Methods and Numerical Examples", arXiv:1208.0628. A poster showcasing this work can be accessed here.