Bayesian analysis of biological networks: clusters, motifs, cross-species correlations

An important part of the analysis of bio-molecular networks is to detect different functional units. Different functions are reflected in a different evolutionary dynamics, and hence in different statistical characteristics of network parts. In this sense, the {\em global statistics} of a biological network, e.g., its connectivity distribution, provides a background, and {\em local deviations} from this background signal functional units. In the computational analysis of biological networks, we thus typically have to discriminate between different statistical models governing different parts of the dataset. The nature of these models depends on the biological question asked. We illustrate this rationale here with three examples: identification of functional parts as highly connected \textit{network clusters}, finding \textit{network motifs}, which occur in a similar form at different places in the network, and the analysis of \textit{cross-species network correlations}, which reflect evolutionary dynamics between species.