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Multilevel delayed acceptance MCMC

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We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the Multilevel MCMC approach of Dodwell et al. (2015) in terms of the Delayed...

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Bibliographic Details
Main Authors: Lykkegaard, Mikkel (Author) , Dodwell, Tim J. (Author) , Fox, Colin (Author) , Mingas, Grigorios (Author) , Scheichl, Robert (Author)
Format: Article (Journal) Chapter/Article
Language:English
Published: 30 Aug 2022
Edition:Version v3
In: Arxiv
Year: 2021, Pages: 1-29
DOI:10.48550/arXiv.2202.03876
Online Access:Verlag, kostenfrei, Volltext: https://doi.org/10.48550/arXiv.2202.03876
Verlag, kostenfrei, Volltext: http://arxiv.org/abs/2202.03876
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Author Notes:Mikkel B. Lykkegaard, Tim J. Dodwell, Colin Fox, Grigorios Mingas, Robert Scheichl
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Summary:We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the Multilevel MCMC approach of Dodwell et al. (2015) in terms of the Delayed Acceptance (DA) MCMC of Christen & Fox (2005). In particular, DA is extended to use a hierarchy of models of arbitrary depth, and allow subchains of arbitrary length. We show that the algorithm satisfies detailed balance, hence is ergodic for the target distribution. Furthermore, multilevel variance reduction is derived that exploits the multiple levels and subchains, and an adaptive multilevel correction to coarse-level biases is developed. Three numerical examples of Bayesian inverse problems are presented that demonstrate the advantages of these novel methods. The software and examples are available in PyMC3.
Item Description:Online veröffentlicht am 8. Februar 2022, Version 2 am 23. August 2022, Version 3 am 30. August 2022. Erscheinungsdatum laut PDF: 5. September 2022
Gesehen am 12.10.2022
Physical Description:Online Resource
DOI:10.48550/arXiv.2202.03876

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