Statistical validation of parametric approximations to the master equation

A number of analytical and Monte Carlo sampling algorithms have been proposed to provide approximate solutions to the master equation. Unfortunately, to maintain accuracy and computational efficiency, most algorithms require specification of well-chosen parameter values. We have recently developed a rigorous statistical hypothesis testing framework that is capable of determining the validity of a given approximation scheme with a specific choice for the parameter values. In this paper, we extend this technique to address the “multiple-testing” problem, in which a set of parameter values is tested simultaneously. This allows for effective tuning of approximation algorithms and for empirically studying the range of validity of a given approximation method.