Bayesian regularization of Gaussian graphical models with measurement error

A framework for determining and estimating the conditional pairwise relationships of variables in high dimensional settings when the observed samples are contaminated with measurement error is proposed. The framework is motivated by the task of establishing gene regulatory networks from microarray studies, in which measurements are taken for a large number of genes from a small sample size, but often measured imperfectly. When no measurement error is present, this problem is often solved by estimating the precision matrix under sparsity constraints. However, when measurement error is present, not correcting for it leads to inconsistent estimates of the precision matrix and poor identification of relationships. To this end, a recent iterative imputation technique developed in the context of missing data is utilized to correct for the biases in the estimates imposed from the contamination. This technique is showcased with a recent variant of the spike-and-slab Lasso to obtain a point estimate of the precision matrix. Simulation studies show that the new method outperforms the naïve method that ignores measurement error in both identification and estimation accuracy. The new method is applied to establish a conditional gene network from a microarray dataset.