We describe the application of the semi-grand canonical Monte Carlo (SGMC) method to analyze and interpret experimental data for nonequilibrium polymer melts and glasses. Experiments that provide information about atomic-level ordering, e.g., birefringence, are amenable to this approach. Closure of the inverse problem of determining the structural detail from limited data is achieved by selecting the lowest-free-energy ensemble of configurations that reproduces the experimental data. The free energy is calculated using the thermodynamic potential of the appropriate semi-grand canonical (SGC) ensemble [NPT Delta mu(I)], as defined by the experimental data. To illustrate the method, we examine uniaxially oriented polyethylene melts of average chain length up to C-400. The simulation results are analyzed for features not explicitly measured by birefringence, such as the density, torsion angle distribution, molecular scale orientation, and free energy, to understand more fully the underlying features of these nonequilibrium states. The stress-optical rule for polyethylene is evaluated in this way.