Selection of Statistical Thresholds in Graphical Models

Reconstruction of gene regulatory networks based on experimental data usually relies on statistical evidence, necessitating the choice of a statistical threshold which defines a significant biological effect. Approaches to this problem found in the literature range from rigorous multiple testing procedures to ad hoc P-value cut-off points. However, when the data implies graphical structure, it should be possible to exploit this feature in the threshold selection process. In this article we propose a procedure based on this principle. Using coding theory we devise a measure of graphical structure, for example, highly connected nodes or chain structure. The measure for a particular graph can be compared to that of a random graph and structure inferred on that basis. By varying the statistical threshold the maximum deviation from random structure can be estimated, and the threshold is then chosen on that basis. A global test for graph structure follows naturally.