A Metropolis-Hastings-Within-Gibbs Sampler for Nonlinear Hierarchical-Bayesian Inverse Problems

John Bardsley, Tiangang Cui

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research

Abstract

We investigate the use of the randomize-then-optimize (RTO) method as a proposal distribution for sampling posterior distributions arising in nonlinear, hierarchical Bayesian inverse problems. Specifically, we extend the hierarchical Gibbs sampler for linear inverse problems to nonlinear inverse problems by embedding RTO-MH within the hierarchical Gibbs sampler. We test the method on a nonlinear inverse problem arising in differential equations.
Original languageEnglish
Title of host publication2017 MATRIX Annals
EditorsDavid R Wood, Jan de Gier, Cheryl E Praeger, Terence Tao
Place of PublicationCham Switzerland
PublisherSpringer
Chapter1
Pages2-12
Number of pages10
Volume2
ISBN (Electronic)9783030041618
ISBN (Print)9783030041601
DOIs
Publication statusPublished - 2019

Publication series

NameMATRIX Book Series
PublisherSpringer Nature Switzerland
Volume2
ISSN (Print)2523-3041
ISSN (Electronic)2523-305X

Cite this

Bardsley, J., & Cui, T. (2019). A Metropolis-Hastings-Within-Gibbs Sampler for Nonlinear Hierarchical-Bayesian Inverse Problems. In D. R. Wood, J. de Gier, C. E. Praeger, & T. Tao (Eds.), 2017 MATRIX Annals (Vol. 2, pp. 2-12). (MATRIX Book Series; Vol. 2). Cham Switzerland: Springer. https://doi.org/10.1007/978-3-030-04161-8_1
Bardsley, John ; Cui, Tiangang. / A Metropolis-Hastings-Within-Gibbs Sampler for Nonlinear Hierarchical-Bayesian Inverse Problems. 2017 MATRIX Annals. editor / David R Wood ; Jan de Gier ; Cheryl E Praeger ; Terence Tao. Vol. 2 Cham Switzerland : Springer, 2019. pp. 2-12 (MATRIX Book Series).
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Bardsley, J & Cui, T 2019, A Metropolis-Hastings-Within-Gibbs Sampler for Nonlinear Hierarchical-Bayesian Inverse Problems. in DR Wood, J de Gier, CE Praeger & T Tao (eds), 2017 MATRIX Annals. vol. 2, MATRIX Book Series, vol. 2, Springer, Cham Switzerland, pp. 2-12. https://doi.org/10.1007/978-3-030-04161-8_1

A Metropolis-Hastings-Within-Gibbs Sampler for Nonlinear Hierarchical-Bayesian Inverse Problems. / Bardsley, John; Cui, Tiangang.

2017 MATRIX Annals. ed. / David R Wood; Jan de Gier; Cheryl E Praeger; Terence Tao. Vol. 2 Cham Switzerland : Springer, 2019. p. 2-12 (MATRIX Book Series; Vol. 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research

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AB - We investigate the use of the randomize-then-optimize (RTO) method as a proposal distribution for sampling posterior distributions arising in nonlinear, hierarchical Bayesian inverse problems. Specifically, we extend the hierarchical Gibbs sampler for linear inverse problems to nonlinear inverse problems by embedding RTO-MH within the hierarchical Gibbs sampler. We test the method on a nonlinear inverse problem arising in differential equations.

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Bardsley J, Cui T. A Metropolis-Hastings-Within-Gibbs Sampler for Nonlinear Hierarchical-Bayesian Inverse Problems. In Wood DR, de Gier J, Praeger CE, Tao T, editors, 2017 MATRIX Annals. Vol. 2. Cham Switzerland: Springer. 2019. p. 2-12. (MATRIX Book Series). https://doi.org/10.1007/978-3-030-04161-8_1

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