AI 中文总结
针对混合不确定性下模型更新中似然难以处理及采样噪声问题，提出基于概率积分变换和最大均值差异的贝叶斯框架，消除重采样噪声，用TMCMC推断，在多个基准上快速完成分析。
AI 中文摘要
混合不确定性下的模型更新具有挑战性，因为偶然输入变异性使模拟器输出为概率分布而非标量，导致似然函数在解析上难以处理。现有的近似贝叶斯计算（ABC）方法通常采用嵌套蒙特卡洛采样，即对每个认知参数评估重新抽取偶然样本，这会在差异度量中引入采样噪声，从而影响后验推断和模型证据。本文通过构造方式消除了这种重采样噪声。概率积分变换（PIT）将随机模拟器转换为关于无分布潜在变量和认知参数的确定性映射。通过冻结一组分层分位数粒子，所得差异度量成为未知参数的确定性、无采样噪声函数。随后采用转移马尔可夫链蒙特卡洛（TMCMC）进行后验推断和模型证据估计。该框架在二维基准问题、高维瞬态振荡器以及NASA兰利多学科不确定性量化挑战的子问题A上得到验证。在标准台式工作站上，完整的贝叶斯分析约在半分钟内完成。
英文摘要
Model updating under hybrid uncertainty is challenging because aleatory input variability makes the simulator output a probability distribution rather than a scalar, rendering the likelihood analytically intractable. Existing Approximate Bayesian Computation (ABC) methods typically employ nested Monte Carlo sampling, where aleatory samples are redrawn for each epistemic parameter evaluation, introducing sampling noise into the discrepancy and consequently affecting posterior inference and model evidence. This paper eliminates this resampling noise by construction. The probability integral transform (PIT) converts the stochastic simulator into a deterministic map of distribution-free latent variables and epistemic parameters. By freezing a set of stratified quantile particles, the resulting discrepancy becomes a deterministic, sampling-noise-free function of the unknown parameters. Transitional Markov Chain Monte Carlo (TMCMC) is then employed for posterior inference and model evidence estimation. The framework is validated on a two-dimensional benchmark, a high-dimensional transient oscillator, and Subproblem A of the NASA Langley Multidisciplinary Uncertainty Quantification Challenge. The complete Bayesian analysis is achieved in approximately half a minute on a standard desktop workstation.
