Large‐Scale Statistical Parameter Estimation in Complex Systems with an Application to Metabolic Models

The estimation of a large number of parameters in a complex dynamic multicompartment model in the presence of insufficient data is a difficult and challenging problem. Such problems arise in many applications, e.g., in biology, physiology, and environmental sciences. The model consists of a large system of coupled nonlinear ordinary differential equations, the data consisting of the values of few components at given observation times. The estimation problems are usually ill‐posed and severely underdetermined, while the quality of the scarce data is far from optimal. Therefore, a successful solution necessarily requires additional information about the parameters. A natural framework to introduce a priori information into the model is the Bayesian paradigm. In this article we develop a Bayesian methodology that is able to utilize various types of prior constraints such as approximate algebraic constraints for the parameters or inequality constraints for the solutions and integrate them into a parametric prior distribution. The subsequent parameter estimation is based on a combination of optimization methods and statistical sampling techniques. We apply the methodology to a skeletal muscle metabolism model, in which we are able to simultaneously estimate more than 100 parameters from one fifth as many measured data points.