Calibration of a radiation quality model for sparse and uncertain data

This article proposes chance-constrained formulations for the calibration of computational models given data subject to uncertainty. The uncertainty might be caused by a poor metrology system, measurement noise, model-form uncertainty or by the inability to directly measure the inputs and/or outputs of the model. The formulations developed, called Forward Maximum Likelihood and Inverse Maximum Likelihood, are applicable to datasets with and without uncertainty. The forward approach performs the calibration in the space of the model's output thereby requiring repeated model simulations. Conversely, the inverse approach leverages an ensemble of solutions to an inverse problem in order to perform the calibration in the space of the model's parameters. The potential loss of performance incurred by this approach is often justified by a sizable reduction in computational cost. The ideas proposed are applied to the calibration of a radiation quality model used by NASA to assess cancer risk in future deep space missions. We calibrate several models in order to evaluate the extent by which data uncertainty, outliers, and the commonly made assumption of parameter independence cause conservatism in the resulting model prediction.