Statistics and Its Interface Volume 6 (2013) 547–558 Inferring metabolic networks using the Bayesian adaptive graphical lasso with informative priors

Metabolic processes are essential for cellular function and survival. We are interested in inferring a metabolic network in activated microglia, a major neuroimmune cell in the brain responsible for the neuroinflammation associated with neurological diseases, based on a set of quantified metabo-lites. To achieve this, we apply the Bayesian adaptive graph-ical lasso with informative priors that incorporate known relationships between covariates. To encourage sparsity, the Bayesian graphical lasso places double exponential priors on the off-diagonal entries of the precision matrix. The Bayesian adaptive graphical lasso allows each double expo-nential prior to have a unique shrinkage parameter. These shrinkage parameters share a common gamma hyperprior. We extend this model to create an informative prior struc-ture by formulating tailored hyperpriors on the shrinkage parameters. By choosing parameter values for each hyper-prior that shift probability mass toward zero for nodes that are close together in a reference network, we encourage edges between covariates with known relationships. This approach can improve the reliability of network inference when the sample size is small relative to the number of parameters to be estimated. When applied to the data on activated microglia, the inferred network includes both known rela-tionships and associations of potential interest for further investigation