title: ExPlanes: exploring planes in triplet data.
abstract: 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.
authors.affiliation: Institut für Mathematik, Angewandte Sekr Holschneider, Universität Potsdam, Campus Golm, Building 28, Karl-Liebknecht-Str 24 D-14476 Potsdam.
authors.forename: Bruno B
authors.initials: BB
authors.lastname: Schwenk
authors.forename: Joachim
authors.initials: J
authors.lastname: Selbig
authors.forename: Yehuda
authors.initials: Y
authors.lastname: Ben-Zion
authors.forename: Matthias
authors.initials: M
authors.lastname: Holschneider
mesh_terms: D017360:Arabidopsis / Q000378:metabolism; D019277:Entropy; D013223:Statistics as Topic / Q000379:methods*