Space instruments rely heavily on modeling to predict and understand the instrument response, enabling a determination of the capabilities and resolution. The Bayesian approach provides a framework to incorporate prior knowledge and propagate uncertainty to predict the instrument response. We present an empirical Bayes model for the end-to-end performance of the Helium, Oxygen, Proton, and Electron (HOPE) mass spectrometers aboard the Van Allen Probes mission. In this model, we use a combination of external modeling, laboratory calibration, and expert opinion to construct the time-of-flight spectra and demonstrate good agreement with on-orbit data. The empirical Bayes model is applied to explore doubly charged ions and carbon, nitrogen, oxygen discrimination during the Van Allen Probes mission.