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.

本文提出了机会受限的公式，用于在给定数据不确定性的情况下对计算模型进行校准。不确定性可能是由于较差的度量系统，测量噪声，模型形式的不确定性或无法直接测量模型的输入和/或输出引起的。开发出的公式称为前向最大似然和逆最大似然，适用于有或没有不确定性的数据集。正向方法在模型输出的空间中执行校准，因此需要重复的模型仿真。相反，为了在模型参数的空间内执行校准，逆方法利用了一组针对逆问题的解决方案。这种方法潜在的性能损失通常可以通过大量降低计算成本来证明。提议的想法被应用于NASA用来评估未来深空任务中的癌症风险的辐射质量模型的校准。我们校准几个模型，以评估数据不确定性，离群值和通常做出的参数独立性假设在结果模型预测中引起保守性的程度。