发表机构
University College Dublin; University College London（都柏林大学学院; 伦敦大学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对多响应贝叶斯校准的后验几何与参数可识别性问题，提出潜变量多响应校准模型，经数值实验与锂电池研究验证其有效性，确立期望费舍尔后验几何为可扩展诊断工具。
AI 中文摘要
模型误设下的校准问题本质上是不适定的，因为在无额外假设时，校准参数与结构偏差在统计上是混淆的。贝叶斯公式通过先验和协方差建模选择（包括多响应观测与跨源对齐）解决这种歧义，但这些选择与依赖输出的不确定性如何共同塑造后验几何及实际参数可识别性，目前仍知之甚少。本文提出一种潜变量多响应校准模型，结合讨厌超参数的经验贝叶斯估计与基于费舍尔信息的校准参数后验的局部高斯近似；针对平方指数和Matérn协方差函数推导了闭式表达式，揭示多响应相关性、潜对齐及输出特定不确定性如何影响局部后验几何。受控数值实验表明，额外响应可为校准参数提供互补的几何约束，而噪声建模可通过降低过度自信提升不确定性量化，却未必改善参数定位；锂离子电池研究进一步说明该模型如何区分强约束与弱约束参数。综上，这些结果确立了期望费舍尔后验几何作为多响应校准中局部参数可识别性的可扩展诊断工具。
英文摘要
Calibration under model misspecification is inherently ill-posed because calibration parameters and structural discrepancy are statistically confounded without additional assumptions. Bayesian formulations address this ambiguity through prior and covariance modeling choices, including multi-response observations and cross-source alignment. However, how these choices, together with output-dependent uncertainty, shape posterior geometry and practical parameter identifiability remains poorly understood. We present a latent-variable multi-response calibration model that combines empirical Bayes estimation of nuisance hyperparameters with a Fisher-information-based local Gaussian approximation of the calibration-parameter posterior. Closed-form expressions are derived for squared-exponential and Matérn covariance functions, revealing how multi-response correlations, latent alignment, and output-specific uncertainty influence local posterior geometry. Controlled numerical experiments show that additional responses provide complementary geometric constraints on calibration parameters, while noise modeling can improve uncertainty quantification by reducing overconfidence without necessarily improving parameter localization. A lithium-ion battery study further illustrates how the model distinguishes strongly from weakly constrained parameters. Together, these results establish expected-Fisher posterior geometry as a scalable diagnostic of local parameter identifiability in multi-response calibration.
