Hybrid Samplers for Ill-Posed Inverse Problems

被引:6
|
作者
Herbei, Radu [1 ]
McKeague, Ian W. [2 ]
机构
[1] Ohio State Univ, Dept Stat, Columbus, OH 43210 USA
[2] Columbia Univ, Dept Biostat, New York, NY 10027 USA
关键词
advection-diffusion; Bayesian regularization; geometric ergodicity; Markov chain Monte Carlo; ocean circulation; random-scan Metropolis; GEOMETRIC ERGODICITY; CIRCULATION;
D O I
10.1111/j.1467-9469.2009.00649.x
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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.
引用
收藏
页码:839 / 853
页数:15
相关论文
共 50 条
  • [1] INVERSE AND ILL-POSED PROBLEMS
    Kabanikhin, S., I
    [J]. SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2010, 7 : C380 - C394
  • [2] LINEAR INVERSE AND ILL-POSED PROBLEMS
    BERTERO, M
    [J]. ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS, 1989, 75 : 1 - 120
  • [3] ILL-POSED INVERSE PROBLEMS IN CHEMISTRY
    Braga, Joao P.
    Lemes, Nelson H. T.
    Borges, Emilio
    Sebastiao, Rita C. O.
    [J]. QUIMICA NOVA, 2016, 39 (07): : 886 - 891
  • [4] Ill-Posed Inverse Problems in Economics
    Horowitz, Joel L.
    [J]. ANNUAL REVIEW OF ECONOMICS, VOL 6, 2014, 6 : 21 - 51
  • [5] INVERSE PROBLEMS AND ILL-POSED PROBLEMS IN GEOPHYSICS
    LUAN, WG
    [J]. ACTA GEOPHYSICA SINICA, 1988, 31 (01): : 108 - 117
  • [6] Inverse Toeplitz preconditioners for ill-posed problems
    Hanke, M
    Nagy, J
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1998, 284 (1-3) : 137 - 156
  • [7] Definitions and examples of inverse and ill-posed problems
    Kabanikhin, S. I.
    [J]. JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2008, 16 (04): : 317 - 357
  • [8] OPTIMALITY IN THE REGULARIZATION OF ILL-POSED INVERSE PROBLEMS
    DAVIES, AR
    HASSAN, MF
    [J]. ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS, 1987, : 553 - 562
  • [9] Ill-posed and inverse problems for hyperbolic equations
    Lavrent'Ev, MM
    [J]. ILL-POSED AND NON-CLASSICAL PROBLEMS OF MATHEMATICAL PHYSICS AND ANALYSIS, PROCEEDINGS, 2003, : 81 - 101
  • [10] Regularized Posteriors in Linear Ill-Posed Inverse Problems
    Florens, Jean-Pierre
    Simoni, Anna
    [J]. SCANDINAVIAN JOURNAL OF STATISTICS, 2012, 39 (02) : 214 - 235