Recent technological advances have made it possible to simultaneously measuremultiple protein activities at the single cell level. With such data collectedunder different stimulatory or inhibitory conditions, it is possible to inferthe causal relationships among proteins from single cell interventional data.In this article we propose a Bayesian hierarchical modeling framework to inferthe signaling pathway based on the posterior distributions of parameters in themodel. Under this framework, we consider network sparsity and model theexistence of an association between two proteins both at the overall levelacross all experiments and at each individual experimental level. This allowsus to infer the pairs of proteins that are associated with each other and theircausal relationships. We also explicitly consider both intrinsic noise andmeasurement error. Markov chain Monte Carlo is implemented for statisticalinference. We demonstrate that this hierarchical modeling can effectively poolinformation from different interventional experiments through simulationstudies and real data analysis.
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