基于贝叶斯委员会机的分层贝叶斯校准
Hierarchical Bayesian Calibration with Bayesian Committee Machine
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中文总结 AI 辅助
针对粒子加速器实验的不确定性量化挑战，提出分层贝叶斯校准框架，结合贝叶斯委员会机实现高效计算，在基准问题和加速器模拟数据上验证了其计算节省与稳健校准性能。
中文摘要 AI 辅助
将计算模型校准到实验数据是应用统计学的核心任务，尤其在科学领域，物理实验成本高昂，模拟在设计和推断中发挥核心作用。受粒子加速器实验中不确定性量化挑战的驱动，我们开发并评估了分层贝叶斯校准（Hierarchical Bayesian Calibration）框架。与标准贝叶斯校准不同，某些输入（如束流注入振幅）必须针对每个实验单独估计。我们采用Kennedy-O'Hagan公式，并通过分层先验结构对特定实验校准参数的分布进行扩展，从而借用重复实验的强度并提升泛化能力。一个关键的方法学挑战来自需要评估大量正向模拟，这使得传统马尔可夫链蒙特卡洛（Markov chain Monte Carlo）方法在计算上不可行。为解决该问题，我们利用贝叶斯委员会机（Bayesian Committee Machine, BCM）作为高斯过程模拟器的可扩展建模策略。BCM提供了一种原则性的分而治之方法，支持并行推理并降低计算成本，无需对模拟器近似进行特定问题的调整。后验采样使用无-U形转弯采样器（No-U-Turn Sampler）执行，该采样器由Julia语言中的自动微分支持，无需解析梯度推导并促进灵活的模型指定。我们使用既定基准问题和阿贡尾场加速器（Argonne Wakefield Accelerator）的模拟数据评估所提出的框架。结果显示出显著的计算节省和稳健的校准性能，凸显了该方法在大规模科学建模问题中的适用性。
英文摘要
Calibrating computational models to experimental data is a core task in applied statistics, especially in scientific domains, where physical experiments are costly and simulations play a central role in design and inference. Motivated by uncertainty quantification challenges in particle accelerator experiments, we develop and evaluate a Hierarchical Bayesian Calibration framework. In contrast to standard Bayesian calibration, certain inputs - such as beam injection amplitude - must be estimated separately for each experiment. We adopt the Kennedy-O'Hagan formulation and extend it with a hierarchical prior structure to model the distribution of experiment-specific calibration parameters, thus borrowing strength and improving generalisation across repeated experiments. A key methodological challenge arises from the need to evaluate a large number of forward simulations, which renders conventional Markov chain Monte Carlo approaches computationally prohibitive. To address this, we leverage the Bayesian Committee Machine as a scalable modelling strategy for Gaussian Process emulators. The BCM provides a principled divide-and-conquer approach, enabling parallel inference and reducing computational cost without requiring problem-specific tuning of the emulator approximation. Posterior sampling is performed using the No-U-Turn Sampler, supported by automatic differentiation in Julia, which removes the need for analytic gradient derivation and facilitates flexible model specification. We assess the proposed framework using established benchmark problems and simulated data from the Argonne Wakefield Accelerator. The results demonstrate substantial computational savings and robust calibration performance, highlighting the applicability of the method to large-scale scientific modelling problems.
