ExPlanes: exploring planes in triplet data.
Many methods for the analysis of gene expression-, protein- or metabolite-data focus on the investigation of binary relationships, while the underlying biological processes creating this data may generate relations of higher than bivariate complexity. We give a novel method ExPlanes that helps to explore certain types of ternary relationships in a statistically robust, Bayesian framework. To arrive at an characterization of the data structure contained in triplet data we investigate 2-dimensional planes being the only linear structures that cannot be inferred from projections of the data. The key part of our methodology is the definition of a robust, Bayesian plane posterior under the assumption of an invariant prior and a Gaussian error model. A numerical representation of the plane posterior can be explored interactively. Beyond this purely Bayesian approach we can use the plane posterior to construct a family of posterior-based test statistics that allow testing the data for different plane related hypotheses. To demonstrate practicability we queried triplets of metabolic data from a plant crossing experiment for the presence of plane-, line- and point-structures by using posterior-based test statistics and were able to show their distinctiveness.
Schwenk
Bruno B
BB
Institut für Mathematik, Angewandte Sekr Holschneider, Universität Potsdam, Campus Golm, Building 28, Karl-Liebknecht-Str 24 D-14476 Potsdam.
Selbig
Joachim
J
Ben-Zion
Yehuda
Y
Holschneider
Matthias
M
D017360:Arabidopsis / Q000378:metabolism; D019277:Entropy; D013223:Statistics as Topic / Q000379:methods*