Bayesian model for uncertainty in the HOPE Mass Spectrometer time-of-flight matrix

Uncertainly quantification is typically thought of as a modeling or prediction field, instrumentation however also relies heavily on modeling to predict response that either cannot or is not feasible to fully constrain in the laboratory. That modeling may be SRIM, SIMION, Geant4, MCNP, or custom depending on the application, but somewhere in the understanding of collected data the model and its uncertainties enter. Then directly leading to largely ignored systematic measurement uncertainty. To address uncertainty in the interpretation of the time-of-flight (TOF) matrix that allows ion species determination we develop and present an empirical Bayesian model for the end-to-end performance of the Helium, Oxygen, Proton, and Electron (HOPE) Mass Spectrometer for the Van Allen Radiation Belt Storm Probes mission. Through this model we utilize a combination of external modeling, laboratory calibration, and expert opinion to construct the time-of-flight spectra from as close to basic measurements as possible and demonstrate good agreement to on-orbit data. The model includes the electrostatic analyzer energy spread, post-acceleration uncertainties, ion/foil scattering and energy straggling, real instrument geometry effects, measured electronics jitter, and laboratory measured detection jitter. Through this model, we explore carbon, nitrogen, oxygen discrimination, heavy ion signatures, and overlap in species determination to provide insight into the data returned during the Van Allen Probes mission.