Recent technological advances have made it possible to simultaneously measure
multiple protein activities at the single cell level. With such data collected
under different stimulatory or inhibitory conditions, it is possible to infer
the causal relationships among proteins from single cell interventional data.
In this article we propose a Bayesian hierarchical modeling framework to infer
the signaling pathway based on the posterior distributions of parameters in the
model.
Ordinary differential equations (ODEs) are commonly used to model dynamic
behavior of a system. Because many parameters are unknown and have to be
estimated from the observed data, there is growing interest in statistics to
develop efficient estimation procedures for these parameters. Among the
proposed methods in the literature, the generalized profiling estimation method
developed by Ramsay and colleagues is particularly promising for its
computational efficiency and good performance. In this approach, the ODE
solution is approximated with a linear combination of basis functions.