Fast and accurate predictions of uncertainties in the computed dose are crucial for the determination of robust treatment plans in radiation therapy. This requires the solution of particle transport problems with uncertain parameters or initial conditions. Monte Carlo methods are often used to solve transport problems especially for applications which require high accuracy. In these cases, common non-intrusive solution strategies that involve repeated simulations of the problem at different points in the parameter space quickly become infeasible due to their long run-times. Intrusive methods however limit the usability in combination with proprietary simulation engines. In our previous paper [51], we demonstrated the application of a new non-intrusive uncertainty quantification approach for Monte Carlo simulations in proton dose calculations with normally distributed errors on realistic patient data. In this paper, we introduce a generalized formulation and focus on a more in-depth theoretical analysis of this method concerning bias, error and convergence of the estimates. The multivariate input model of the proposed approach further supports almost arbitrary error correlation models. We demonstrate how this framework can be used to model and efficiently quantify complex auto-correlated and time-dependent errors.

翻译：对计算剂量不确定性的快速和准确预测对于确定辐射疗法的稳健治疗计划至关重要。这要求用不确定的参数或初始条件解决粒子迁移问题。蒙特卡洛方法常常用于解决运输问题,特别是需要高度精确的应用程序。在这些情况下,共同的非侵入性解决办法战略,涉及在参数空间不同点反复模拟问题,由于其长期的运行时间,很快变得不可行。侵入方法却限制了与专利模拟引擎相结合的可用性。在先前的文件中[51],我们展示了在计算质子剂量时对蒙特卡洛模拟采用新的非侵入性不确定性量化方法,通常在现实的病人数据上出现差错。在本文中,我们采用了一种通用的提法,侧重于对这种方法进行更深入的理论分析,涉及偏差、误差和估计数的汇合。拟议方法的多变量输入模型进一步支持几乎武断的误差相关模型。我们展示了如何使用这一框架来模拟和有效地量化复杂的自动相关和时间错误。