结构不可识别模型中参数推断的马尔可夫链蒙特卡罗方法
MCMC Methods for Parameter Inference in Structurally Nonidentifiable Models
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中文总结 AI 辅助
针对结构不可识别的ODE模型参数推断问题，开发了可识别性感知几何MCMC和可识别性感知伪边际MCMC两种方法，利用结构可识别性分析信息，提高采样效率和收敛性，且都针对正确后验分布，在标准条件下遍历。
中文摘要 AI 辅助
我们考虑具有结构不可识别性的常微分方程（ODE）模型的参数推断问题。此类模型出现在包括控制理论、系统生物学和公共卫生等广泛科学领域。当不同参数值产生相同模型输出时会出现结构不可识别性，导致参数空间中观测等效解的低维流形。这给贝叶斯推断和马尔可夫链蒙特卡罗（MCMC）方法带来挑战，常导致混合不佳和收敛缓慢。我们开发了两种利用结构可识别性分析信息的MCMC方法。第一种是可识别性感知几何MCMC，在不可识别流形内和之间构造提议。第二种是可识别性感知伪边际MCMC，对可识别参数组合空间进行推断并重建完整参数值。我们表明两种方法都针对正确的后验分布，并且在标准条件下是遍历的。数值示例表明与标准MCMC方法相比，采样效率和收敛性有所提高。
英文摘要
We consider the problem of parameter inference for ordinary differential equation (ODE) models with structural non-identifiability. Such models arise in a wide range of scientific fields, including control theory, systems biology, and public health. Structural non-identifiability occurs when distinct parameter values provide identical model outputs, resulting in lower-dimensional manifolds of observationally equivalent solutions in the parameter space. This poses challenges for Bayesian inference and Markov chain Monte Carlo (MCMC) methods, often leading to poor mixing and slow convergence. We develop two MCMC methods that use information from structural identifiability analysis. The first, Identifiability-Aware Geometric MCMC, constructs proposals that move within and between non-identifiable manifolds. The second, Identifiability-Aware Pseudo-Marginal MCMC, performs inference on the space of identifiable parameter combinations and reconstructs full parameter values. We show that both methods target the correct posterior distribution and are ergodic under standard conditions. Numerical examples demonstrate improved sampling efficiency and convergence compared with standard MCMC methods.
