Tests for Gaussian graphical models

Gaussian graphical models are promising tools for analysing genetic networks. In many applications, biologists have some knowledge of the genetic network and may want to assess the quality of their model using gene expression data. This is why one introduces a novel procedure for testing the neighborhoods of a Gaussian graphical model. It is based on the connection between the local Markov property and conditional regression of a Gaussian random variable. Adapting recent results on tests for high-dimensional Gaussian linear models, one proves that the testing procedure inherits appealing theoretical properties. Besides, it applies and is computationally feasible in a high-dimensional setting: the number of nodes may be much larger than the number of observations. A large part of the study is devoted to illustrating and discussing applications to simulated data and to biological data.