推理后模型链式连接：问题陈述与面向端到端数字孪生训练的基于模型的Bootstrap
Post-Inference Model Chaining: A Problem Statement and a Model-based Bootstrap for Training End-to-End Digital Twins
Lukas Madenach, Timo Bailer, Tobias Eilert
AI 速览：作者指出，在端到端数字孪生中，将完整预测抽样沿各阶段模型链式前向传递的常用Monte Carlo方案会导致区间与覆盖率膨胀，并提出一种基于模型的Bootstrap来改善末端预测。
End-to-end digital twins can be constructed by fitting separate stage models and connecting them after inference. We investigate the Frequentist prediction properties of a commonly used Monte Carlo simulation scheme that forwards complete predictive draws through such a chain when measured stage outputs contain independent normal errors, but the latent stage means are deterministic. Analytical two-stage examples show persistent asymptotic interval and coverage inflation and, with quadratic propagation, mean bias dependent on the parameters to be estimated. Simulations of four- and eight-stage linear-quadratic univariate chains with 7, 15 or 30 training runs demonstrate pronounced input-dependent distortions. A diagnostic using error-free latent training predictors shows that the effect is mainly not attributable to errors in variables, but to the MCSim approach even showing underestimation of coverage. We propose a model-based bootstrap: an initial chain forwards fitted means, bootstrap chains are refitted on fixed-center bootstrap data while forwarding their mean prediction, and a target-stage future error enters a studentized prediction root. Across the investigated scenarios, relative mean bias is substantially reduced, and coverage is closer to the nominal 90%. At sample size 30, the eight-stage bootstrap has mean width ratios of 1.16-1.42 relative to the known-parameter normal reference, compared with 4.11-4.97 for observed-to-observed MCSim. These results support improved endpoint prediction in the tested setting. Further investigations of the bootstrap scheme in the supplement for a bivariate 6-stage process show similar satisfactory results.