In biological experiments researchers often have information in the form of a
graph that supplements observed numerical data. Incorporating the knowledge
contained in these graphs into an analysis of the numerical data is an
important and nontrivial task. We look at the example of metagenomic
data---data from a genomic survey of the abundance of different species of
bacteria in a sample. Here, the graph of interest is a phylogenetic tree
depicting the interspecies relationships among the bacteria species. We
illustrate that analysis of the data in a nonstandard inner-product space
effectively uses this additional graphical information and produces more
meaningful results.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS402 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
