标题： 具有高斯级数先验的初始热状态的贝叶斯推理 显示英文标题

标题： Bayesian Inference for Initial Heat States with Gaussian Series Priors

摘要： 我们考虑从固定时间点热方程解的非均匀域内的噪声内部测量中恢复未知初始热状态的统计线性反问题。 我们采用基于 Dirichlet-Laplacian 特征基定义的高斯级数先验的非参数贝叶斯方法，得到具有明确后验推断表达式的方便的共轭后验分布。 我们回顾了最近的理论结果，这些结果在大样本量极限下提供了由此产生的基于后验点估计和不确定性量化的方法的渐近性能保证。 我们进一步提供了该方法的实现，并通过数值模拟研究进行了说明。 显示英文摘要

摘要： We consider the statistical linear inverse problem of recovering the unknown initial heat state from noisy interior measurements over an inhomogeneous domain of the solution to the heat equation at a fixed time instant. We employ nonparametric Bayesian procedures with Gaussian series priors defined on the Dirichlet-Laplacian eigenbasis, yielding convenient conjugate posterior distributions with explicit expressions for posterior inference. We review recent theoretical results that provide asymptotic performance guarantees (in the large sample size limit) for the resulting posterior-based point estimation and uncertainty quantification. We further provide an implementation of the approach, and illustrate it via a numerical simulation study.