Randomized approaches to accelerate MCMC algorithms for Bayesian inverse problems
Randomized approaches to accelerate MCMC algorithms for Bayesian inverse problems
复制标题
加速贝叶斯逆问题 MCMC 算法的随机方法
DOI：
10.1016/j.jcp.2021.110391
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发表时间：
2021
影响因子：
4.1
通讯作者：
Kilmer, Misha E.
中科院分区：
文献类型：
--
作者：
Saibaba, Arvind K.;Prasad, Pranjal;de Sturler, Eric;Miller, Eric;Kilmer, Misha E.
马尔可夫链蒙特卡罗（MCMC）方法传统上用于逆问题中的不确定性量化，其中底层传感器模态的物理学由偏微分方程（PDE）描述。然而，在每个对数似然评估可能需要与多个传感器相对应的数百到数千次偏微分方程求解的应用中，使用MCMC算法的成本极其昂贵;即，空间分布的源和接收器可能根据精确的应用而工作在不同的频率或波长。我们展示了如何减轻计算成本的每个对数似然评估，通过使用几种随机技术，并嵌入这些随机近似MCMC算法。由此产生的MCMC算法是计算效率高的方法，用于量化与重构参数相关联的不确定性。我们证明了我们提出的算法的精度和计算的好处，从漫射光学层析成像的模型应用，我们反转的光吸收的空间分布。
Markov chain Monte Carlo (MCMC) approaches are traditionally used for uncertainty quantification in inverse problems where the physics of the underlying sensor modality is described by a partial differential equation (PDE). However, the use of MCMC algorithms is prohibitively expensive in applications where each log-likelihood evaluation may require hundreds to thousands of PDE solves corresponding to multiple sensors; i.e., spatially distributed sources and receivers perhaps operating at different frequencies or wavelengths depending on the precise application. We show how to mitigate the computational cost of each log-likelihood evaluation by using several randomized techniques and embed these randomized approximations within MCMC algorithms. The resulting MCMC algorithms are computationally efficient methods for quantifying the uncertainty associated with the reconstructed parameters. We demonstrate the accuracy and computational benefits of our proposed algorithms on a model application from diffuse optical tomography where we invert for the spatial distribution of optical absorption.