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Multilevel dimension-independent likelihood-informed MCMC for large-scale inverse problems

We present a non-trivial integration of dimension-independent likelihood-informed (DILI) MCMC (Cui et al 2016) and the multilevel MCMC (Dodwell et al 2015) to explore the hierarchy of posterior distributions. This integration offers several advantages: First, DILI-MCMC employs an intrinsic likelihoo...

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Hauptverfasser: Cui, Tiangang (VerfasserIn) , Detommaso, Gianluca (VerfasserIn) , Scheichl, Robert (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 5 February 2024
In: Inverse problems
Year: 2024, Jahrgang: 40, Heft: 3, Pages: 1-33
ISSN:1361-6420
DOI:10.1088/1361-6420/ad1e2c
Online-Zugang:Verlag, kostenfrei, Volltext: https://doi.org/10.1088/1361-6420/ad1e2c
Verlag, kostenfrei, Volltext: https://dx.doi.org/10.1088/1361-6420/ad1e2c
Volltext
Verfasserangaben:Tiangang Cui, Gianluca Detommaso and Robert Scheichl
Beschreibung
Zusammenfassung:We present a non-trivial integration of dimension-independent likelihood-informed (DILI) MCMC (Cui et al 2016) and the multilevel MCMC (Dodwell et al 2015) to explore the hierarchy of posterior distributions. This integration offers several advantages: First, DILI-MCMC employs an intrinsic likelihood-informed subspace (LIS) (Cui et al 2014)—which involves a number of forward and adjoint model simulations—to design accelerated operator-weighted proposals. By exploiting the multilevel structure of the discretised parameters and discretised forward models, we design a Rayleigh-Ritz procedure to significantly reduce the computational effort in building the LIS and operating with DILI proposals. Second, the resulting DILI-MCMC can drastically improve the sampling efficiency of MCMC at each level, and hence reduce the integration error of the multilevel algorithm for fixed CPU time. Numerical results confirm the improved computational efficiency of the multilevel DILI approach.
Beschreibung:Gesehen am 17.06.2024
Beschreibung:Online Resource
ISSN:1361-6420
DOI:10.1088/1361-6420/ad1e2c

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