Computer models are widely used in science and engineering to simulate complex systems. However, these models are affected by several sources of uncertainty, which may limit their use for decision making in risk management. We present a Bayesian approach for quantifying parameter uncertainty in a chain of two computer models motivated by multiphysics simulations in the nuclear field. Part of the inputs of a downstream model parametrized by $θ\in \mathbb{R}^p$ come from the outputs of an upstream model parametrized by $λ\in \mathbb{R}^q$. Usually, the joint posterior distribution of $(θ, λ)$ would be obtained by applying Bayes' theorem using the experimental observations of both models. However, when the observations of the downstream model are too indirect to provide informative inference on $λ$, it may be preferable to compute a modular posterior distribution of $(θ, λ)$, referred to as the \emph{cut distribution}. Assuming that the posterior distribution of $λ$ has been previously estimated from observations of the upstream model only, we aim to compute the posterior distribution of $θ$ conditional on $λ$ using observations from the downstream model. To this end, we propose a Gaussian-process and linear-based framework to estimate the functional dependence between $θ$ and $λ$, denoted by $θ(λ)$, where each component is modeled as a realization of a Gaussian process. As the downstream model is approximated by a linear function of $θ(λ)$, Bayesian conjugacy allows us to derive a Gaussian posterior predictive distribution of $θ(λ)$ for any realization of $λ$. The effectiveness of the method is illustrated through several synthetic examples, and we highlight how variations in $λ$ impact the predictive distribution of the chained simulation.

翻译：计算机模型在科学与工程领域被广泛用于模拟复杂系统。然而，这些模型受到多种不确定性来源的影响，可能限制其在风险管理决策中的应用。本文提出一种贝叶斯方法，用于量化核能领域多物理场模拟所驱动的链式双计算机模型中的参数不确定性。下游模型（以 $θ\in \mathbb{R}^p$ 参数化）的部分输入来源于上游模型（以 $λ\in \mathbb{R}^q$ 参数化）的输出。通常，$(θ, λ)$ 的联合后验分布可通过贝叶斯定理结合两个模型的实验观测数据获得。然而，当下游模型的观测数据过于间接而无法对 $λ$ 提供有效推断时，更适宜计算 $(θ, λ)$ 的模块化后验分布，即\emph{截断分布}。在假设已通过仅上游模型观测数据估计出 $λ$ 的后验分布的前提下，我们旨在利用下游模型观测数据计算 $θ$ 关于 $λ$ 的条件后验分布。为此，我们提出一种基于高斯过程与线性模型的框架，用于估计 $θ$ 与 $λ$ 之间的函数依赖关系（记为 $θ(λ)$），其中每个分量被建模为高斯过程的实现。由于下游模型通过 $θ(λ)$ 的线性函数进行近似，贝叶斯共轭性使我们能够推导出任意 $λ$ 实现对应的 $θ(λ)$ 高斯后验预测分布。通过多个合成算例验证了该方法的有效性，并重点展示了 $λ$ 的变化如何影响链式模拟的预测分布。