关于预条件Crank-Nicolson Metropolis算法的推广
On a generalization of the preconditioned Crank-Nicolson Metropolis algorithm
AI总结：
本文提出一种改进的预条件Crank-Nicolson Metropolis算法，用于无限维Hilbert空间概率测度近似采样，并展示其在贝叶斯反问题中的有效性，证明其与状态空间维度和观测噪声方差无关，且具有几何混合性。
摘要：
本文考虑了用于无限维Hilbert空间概率测度近似采样的Metropolis算法，并引入了预条件Crank-Nicolson（pCN）提议的推广。新的提议能够结合目标测度的信息。一个贝叶斯反问题的数值模拟表明，具有此类提议的Metropolis算法在状态空间维度和观测噪声方差方面表现独立。此外，通过谱间隙的比较论证提供了定性收敛结果。特别是，证明了该推广继承了pCN提议的Metropolis算法的几何混合性。
英文摘要：
Metropolis algorithms for approximate sampling of probability measures on infinite dimensional Hilbert spaces are considered and a generalization of the preconditioned Crank-Nicolson (pCN) proposal is introduced. The new proposal is able to incorporate information of the measure of interest. A numerical simulation of a Bayesian inverse problem indicates that a Metropolis algorithm with such a proposal performs independent of the state space dimension and the variance of the observational noise. Moreover, a qualitative convergence result is provided by a comparison argument for spectral gaps. In particular, it is shown that the generalization inherits geometric ergodicity from the Metropolis algorithm with pCN proposal.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
