Hybrid Samplers for Ill‐Posed Inverse Problems
Hybrid Samplers for Ill‐Posed Inverse Problems
复制标题
用于不适定逆问题的混合采样器
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
I. McKeague
中科院分区：
文献类型：
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作者：
Radu Herbei;I. McKeague
摘要：在求解不适定反问题的贝叶斯方法中，正则化是通过指定感兴趣参数的先验分布来实现的，马尔可夫链蒙特卡罗采样器用于提取有关其后验分布的信息。 研究了不适定反问题中后验分布的随机扫描随机行走大都会（RSM）算法的收敛性.我们提供了一个可访问的充分条件，在观察模型和先验，以确保几何遍历的后验分布的RSM采样。我们说明了如何在海洋示踪剂数据反演的应用程序中检查这些条件。
Abstract. In the Bayesian approach to ill‐posed inverse problems, regularization is imposed by specifying a prior distribution on the parameters of interest and Markov chain Monte Carlo samplers are used to extract information about its posterior distribution. The aim of this paper is to investigate the convergence properties of the random‐scan random‐walk Metropolis (RSM) algorithm for posterior distributions in ill‐posed inverse problems. We provide an accessible set of sufficient conditions, in terms of the observational model and the prior, to ensure geometric ergodicity of RSM samplers of the posterior distribution. We illustrate how these conditions can be checked in an application to the inversion of oceanographic tracer data.