Gene regulatory networks (GRNs) encode interactions within cells that control the expression levels of genes, and thereby, proteins. GRNs have been shown to play a vital role in both normal cellular function and malignancy. Despite this, there are few statistical methods for estimating GRNs from gene expression measurements. Further, most available methods focus upon delivering a single network estimate by maximizing efficiency in examining the vast space of possible networks. Rather than one estimate, we propose a ternary mixture model with likelihood based scores designed to deliver a posterior distribution of possible networks. Our method is demonstrated on qPCR data from single perturbation experiments conducted in murine cancer cell lines.