Network structure is a dominant feature of many biological systems, both at the cellular level and within natural populations. Advances in genotype and gene expression screening made over the last few decades have permitted the reconstruction of these networks. However, resolution to a single model estimate will generally not be possible, leaving open the question of the appropriate method of formal statistical inference. The nonstandard structure of the problem precludes most traditional statistical methodologies. Alternatively, a Bayesian approach provides a natural methodology for formal inference. Construction of a posterior density on the space of network structures allows formal inference regarding features of network structure using specific marginal posterior distributions.
An information theoretic approach to this problem will be described, based on the Minimum Description Length principle. This leads to a Bayesian inference model based on the information content of data rather than on more commonly used probabilistic models. The approach is applied to the problem of pedigree reconstruction based on genotypic data. Using this application, it is shown how the MDL approach is able to provide a truly objective control for model complexity.
A two-cohort model is used for a simulation study. The MDL approach is compared to COLONY-2, a well known pedigree reconstruction application. The study highlights the problem of genotyping error modeling. COLONY-2 requires prior error rate estimates, and its accuracy proves to be highly sensitive to these estimates. In contrast, the MDL approach does not require prior error rate estimates, and is able to accurately adjust for genotyping error across the range of models considered.
