论文标题
PYMC3中具有自适应误差模型的多级延迟接受MCMC
Multilevel Delayed Acceptance MCMC with an Adaptive Error Model in PyMC3
论文作者
论文摘要
通过马尔可夫链蒙特卡洛（MCMC）进行不确定性定量，对于具有昂贵似然函数的目标概率密度的昂贵，例如，当评估涉及解决部分微分方程（PDE）时，就像在广泛的工程应用程序中一样。具有自适应误差模型（AEM）的多级延迟接受（MLDA）是一种新颖的方法，它通过利用模型的层次结构来减轻此问题，并以增加的复杂性和成本，并在现实中纠正廉价的模型。该方法已集成到开源概率编程软件包PYMC3中，并在最新开发版本中可用。在本文中，将算法与一个说明性示例一起介绍。
Uncertainty Quantification through Markov Chain Monte Carlo (MCMC) can be prohibitively expensive for target probability densities with expensive likelihood functions, for instance when the evaluation it involves solving a Partial Differential Equation (PDE), as is the case in a wide range of engineering applications. Multilevel Delayed Acceptance (MLDA) with an Adaptive Error Model (AEM) is a novel approach, which alleviates this problem by exploiting a hierarchy of models, with increasing complexity and cost, and correcting the inexpensive models on-the-fly. The method has been integrated within the open-source probabilistic programming package PyMC3 and is available in the latest development version. In this paper, the algorithm is presented along with an illustrative example.
