  Motivated by inferring cellular signaling networks using noisy flow cytometry
data, we develop procedures to draw inference for Bayesian networks based on
error-prone data. Two methods for inferring causal relationships between nodes
in a network are proposed based on penalized estimation methods that account
for measurement error and encourage sparsity. We discuss consistency of the
proposed network estimators and develop an approach for selecting the tuning
parameter in the penalized estimation methods. Empirical studies are carried
out to compare the proposed methods and a naive method that ignores measurement
error with applications to synthetic data and to single cell flow cytometry
data.
