Solving Geophysical Inversion Problems with Intractable Likelihoods: Linearized Gaussian Approximations Versus the Correlated Pseudo-marginal Method
Abstract A geophysical Bayesian inversion problem may target the posterior distribution of geological or hydrogeological parameters given geophysical data. To account for the scatter in the petrophysical relationship linking the target parameters to the geophysical properties, this study treats the...
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| Autor*in: |
Friedli, Lea [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2023 |
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| Übergeordnetes Werk: |
Enthalten in: Mathematical geology - New York, NY [u.a.] : Springer Science + Business Media B.V., 1969, 56(2023), 1 vom: 02. Juni, Seite 55-75 |
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| Übergeordnetes Werk: |
volume:56 ; year:2023 ; number:1 ; day:02 ; month:06 ; pages:55-75 |
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| DOI / URN: |
10.1007/s11004-023-10064-y |
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| 520 | |a Abstract A geophysical Bayesian inversion problem may target the posterior distribution of geological or hydrogeological parameters given geophysical data. To account for the scatter in the petrophysical relationship linking the target parameters to the geophysical properties, this study treats the intermediate geophysical properties as latent (unobservable) variables. To perform inversion in such a latent variable model, the intractable likelihood function of the (hydro)geological parameters given the geophysical data needs to be estimated. This can be achieved by approximation with a Gaussian probability density function based on local linearization of the geophysical forward operator, thereby, accounting for the noise in the petrophysical relationship by a corresponding addition to the data covariance matrix. The new approximate method is compared against the general correlated pseudo-marginal method, which estimates the likelihood by Monte Carlo averaging over samples of the latent variable. First, the performances of the two methods are tested on a synthetic test example, in which a multivariate Gaussian porosity field is inferred using crosshole ground-penetrating radar first-arrival travel times. For this example with rather small petrophysical uncertainty, the two methods provide near-identical estimates, while an inversion that ignores petrophysical uncertainty leads to biased estimates. The results of a sensitivity analysis are then used to suggest that the linearized Gaussian approach, while attractive due to its relative computational speed, suffers from a decreasing accuracy with increasing scatter in the petrophysical relationship. The computationally more expensive correlated pseudo-marginal method performs very well even for settings with high petrophysical uncertainty. | ||
| 650 | 4 | |a Inverse theory |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Intractable likelihood |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Latent variable model |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Hydrogeophysics |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Linde, Niklas |4 aut | |
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10.1007/s11004-023-10064-y doi (DE-627)SPR054535077 (SPR)s11004-023-10064-y-e DE-627 ger DE-627 rakwb eng Friedli, Lea verfasserin (orcid)0000-0002-7639-8196 aut Solving Geophysical Inversion Problems with Intractable Likelihoods: Linearized Gaussian Approximations Versus the Correlated Pseudo-marginal Method 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract A geophysical Bayesian inversion problem may target the posterior distribution of geological or hydrogeological parameters given geophysical data. To account for the scatter in the petrophysical relationship linking the target parameters to the geophysical properties, this study treats the intermediate geophysical properties as latent (unobservable) variables. To perform inversion in such a latent variable model, the intractable likelihood function of the (hydro)geological parameters given the geophysical data needs to be estimated. This can be achieved by approximation with a Gaussian probability density function based on local linearization of the geophysical forward operator, thereby, accounting for the noise in the petrophysical relationship by a corresponding addition to the data covariance matrix. The new approximate method is compared against the general correlated pseudo-marginal method, which estimates the likelihood by Monte Carlo averaging over samples of the latent variable. First, the performances of the two methods are tested on a synthetic test example, in which a multivariate Gaussian porosity field is inferred using crosshole ground-penetrating radar first-arrival travel times. For this example with rather small petrophysical uncertainty, the two methods provide near-identical estimates, while an inversion that ignores petrophysical uncertainty leads to biased estimates. The results of a sensitivity analysis are then used to suggest that the linearized Gaussian approach, while attractive due to its relative computational speed, suffers from a decreasing accuracy with increasing scatter in the petrophysical relationship. The computationally more expensive correlated pseudo-marginal method performs very well even for settings with high petrophysical uncertainty. Inverse theory (dpeaa)DE-He213 Intractable likelihood (dpeaa)DE-He213 Latent variable model (dpeaa)DE-He213 Hydrogeophysics (dpeaa)DE-He213 Linde, Niklas aut Enthalten in Mathematical geology New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 56(2023), 1 vom: 02. Juni, Seite 55-75 (DE-627)31827051X (DE-600)2017903-0 1573-8868 nnns volume:56 year:2023 number:1 day:02 month:06 pages:55-75 https://dx.doi.org/10.1007/s11004-023-10064-y kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 AR 56 2023 1 02 06 55-75 |
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10.1007/s11004-023-10064-y doi (DE-627)SPR054535077 (SPR)s11004-023-10064-y-e DE-627 ger DE-627 rakwb eng Friedli, Lea verfasserin (orcid)0000-0002-7639-8196 aut Solving Geophysical Inversion Problems with Intractable Likelihoods: Linearized Gaussian Approximations Versus the Correlated Pseudo-marginal Method 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract A geophysical Bayesian inversion problem may target the posterior distribution of geological or hydrogeological parameters given geophysical data. To account for the scatter in the petrophysical relationship linking the target parameters to the geophysical properties, this study treats the intermediate geophysical properties as latent (unobservable) variables. To perform inversion in such a latent variable model, the intractable likelihood function of the (hydro)geological parameters given the geophysical data needs to be estimated. This can be achieved by approximation with a Gaussian probability density function based on local linearization of the geophysical forward operator, thereby, accounting for the noise in the petrophysical relationship by a corresponding addition to the data covariance matrix. The new approximate method is compared against the general correlated pseudo-marginal method, which estimates the likelihood by Monte Carlo averaging over samples of the latent variable. First, the performances of the two methods are tested on a synthetic test example, in which a multivariate Gaussian porosity field is inferred using crosshole ground-penetrating radar first-arrival travel times. For this example with rather small petrophysical uncertainty, the two methods provide near-identical estimates, while an inversion that ignores petrophysical uncertainty leads to biased estimates. The results of a sensitivity analysis are then used to suggest that the linearized Gaussian approach, while attractive due to its relative computational speed, suffers from a decreasing accuracy with increasing scatter in the petrophysical relationship. The computationally more expensive correlated pseudo-marginal method performs very well even for settings with high petrophysical uncertainty. Inverse theory (dpeaa)DE-He213 Intractable likelihood (dpeaa)DE-He213 Latent variable model (dpeaa)DE-He213 Hydrogeophysics (dpeaa)DE-He213 Linde, Niklas aut Enthalten in Mathematical geology New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 56(2023), 1 vom: 02. Juni, Seite 55-75 (DE-627)31827051X (DE-600)2017903-0 1573-8868 nnns volume:56 year:2023 number:1 day:02 month:06 pages:55-75 https://dx.doi.org/10.1007/s11004-023-10064-y kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 AR 56 2023 1 02 06 55-75 |
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10.1007/s11004-023-10064-y doi (DE-627)SPR054535077 (SPR)s11004-023-10064-y-e DE-627 ger DE-627 rakwb eng Friedli, Lea verfasserin (orcid)0000-0002-7639-8196 aut Solving Geophysical Inversion Problems with Intractable Likelihoods: Linearized Gaussian Approximations Versus the Correlated Pseudo-marginal Method 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract A geophysical Bayesian inversion problem may target the posterior distribution of geological or hydrogeological parameters given geophysical data. To account for the scatter in the petrophysical relationship linking the target parameters to the geophysical properties, this study treats the intermediate geophysical properties as latent (unobservable) variables. To perform inversion in such a latent variable model, the intractable likelihood function of the (hydro)geological parameters given the geophysical data needs to be estimated. This can be achieved by approximation with a Gaussian probability density function based on local linearization of the geophysical forward operator, thereby, accounting for the noise in the petrophysical relationship by a corresponding addition to the data covariance matrix. The new approximate method is compared against the general correlated pseudo-marginal method, which estimates the likelihood by Monte Carlo averaging over samples of the latent variable. First, the performances of the two methods are tested on a synthetic test example, in which a multivariate Gaussian porosity field is inferred using crosshole ground-penetrating radar first-arrival travel times. For this example with rather small petrophysical uncertainty, the two methods provide near-identical estimates, while an inversion that ignores petrophysical uncertainty leads to biased estimates. The results of a sensitivity analysis are then used to suggest that the linearized Gaussian approach, while attractive due to its relative computational speed, suffers from a decreasing accuracy with increasing scatter in the petrophysical relationship. The computationally more expensive correlated pseudo-marginal method performs very well even for settings with high petrophysical uncertainty. Inverse theory (dpeaa)DE-He213 Intractable likelihood (dpeaa)DE-He213 Latent variable model (dpeaa)DE-He213 Hydrogeophysics (dpeaa)DE-He213 Linde, Niklas aut Enthalten in Mathematical geology New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 56(2023), 1 vom: 02. Juni, Seite 55-75 (DE-627)31827051X (DE-600)2017903-0 1573-8868 nnns volume:56 year:2023 number:1 day:02 month:06 pages:55-75 https://dx.doi.org/10.1007/s11004-023-10064-y kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 AR 56 2023 1 02 06 55-75 |
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10.1007/s11004-023-10064-y doi (DE-627)SPR054535077 (SPR)s11004-023-10064-y-e DE-627 ger DE-627 rakwb eng Friedli, Lea verfasserin (orcid)0000-0002-7639-8196 aut Solving Geophysical Inversion Problems with Intractable Likelihoods: Linearized Gaussian Approximations Versus the Correlated Pseudo-marginal Method 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract A geophysical Bayesian inversion problem may target the posterior distribution of geological or hydrogeological parameters given geophysical data. To account for the scatter in the petrophysical relationship linking the target parameters to the geophysical properties, this study treats the intermediate geophysical properties as latent (unobservable) variables. To perform inversion in such a latent variable model, the intractable likelihood function of the (hydro)geological parameters given the geophysical data needs to be estimated. This can be achieved by approximation with a Gaussian probability density function based on local linearization of the geophysical forward operator, thereby, accounting for the noise in the petrophysical relationship by a corresponding addition to the data covariance matrix. The new approximate method is compared against the general correlated pseudo-marginal method, which estimates the likelihood by Monte Carlo averaging over samples of the latent variable. First, the performances of the two methods are tested on a synthetic test example, in which a multivariate Gaussian porosity field is inferred using crosshole ground-penetrating radar first-arrival travel times. For this example with rather small petrophysical uncertainty, the two methods provide near-identical estimates, while an inversion that ignores petrophysical uncertainty leads to biased estimates. The results of a sensitivity analysis are then used to suggest that the linearized Gaussian approach, while attractive due to its relative computational speed, suffers from a decreasing accuracy with increasing scatter in the petrophysical relationship. The computationally more expensive correlated pseudo-marginal method performs very well even for settings with high petrophysical uncertainty. Inverse theory (dpeaa)DE-He213 Intractable likelihood (dpeaa)DE-He213 Latent variable model (dpeaa)DE-He213 Hydrogeophysics (dpeaa)DE-He213 Linde, Niklas aut Enthalten in Mathematical geology New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 56(2023), 1 vom: 02. Juni, Seite 55-75 (DE-627)31827051X (DE-600)2017903-0 1573-8868 nnns volume:56 year:2023 number:1 day:02 month:06 pages:55-75 https://dx.doi.org/10.1007/s11004-023-10064-y kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 AR 56 2023 1 02 06 55-75 |
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10.1007/s11004-023-10064-y doi (DE-627)SPR054535077 (SPR)s11004-023-10064-y-e DE-627 ger DE-627 rakwb eng Friedli, Lea verfasserin (orcid)0000-0002-7639-8196 aut Solving Geophysical Inversion Problems with Intractable Likelihoods: Linearized Gaussian Approximations Versus the Correlated Pseudo-marginal Method 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract A geophysical Bayesian inversion problem may target the posterior distribution of geological or hydrogeological parameters given geophysical data. To account for the scatter in the petrophysical relationship linking the target parameters to the geophysical properties, this study treats the intermediate geophysical properties as latent (unobservable) variables. To perform inversion in such a latent variable model, the intractable likelihood function of the (hydro)geological parameters given the geophysical data needs to be estimated. This can be achieved by approximation with a Gaussian probability density function based on local linearization of the geophysical forward operator, thereby, accounting for the noise in the petrophysical relationship by a corresponding addition to the data covariance matrix. The new approximate method is compared against the general correlated pseudo-marginal method, which estimates the likelihood by Monte Carlo averaging over samples of the latent variable. First, the performances of the two methods are tested on a synthetic test example, in which a multivariate Gaussian porosity field is inferred using crosshole ground-penetrating radar first-arrival travel times. For this example with rather small petrophysical uncertainty, the two methods provide near-identical estimates, while an inversion that ignores petrophysical uncertainty leads to biased estimates. The results of a sensitivity analysis are then used to suggest that the linearized Gaussian approach, while attractive due to its relative computational speed, suffers from a decreasing accuracy with increasing scatter in the petrophysical relationship. The computationally more expensive correlated pseudo-marginal method performs very well even for settings with high petrophysical uncertainty. Inverse theory (dpeaa)DE-He213 Intractable likelihood (dpeaa)DE-He213 Latent variable model (dpeaa)DE-He213 Hydrogeophysics (dpeaa)DE-He213 Linde, Niklas aut Enthalten in Mathematical geology New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 56(2023), 1 vom: 02. Juni, Seite 55-75 (DE-627)31827051X (DE-600)2017903-0 1573-8868 nnns volume:56 year:2023 number:1 day:02 month:06 pages:55-75 https://dx.doi.org/10.1007/s11004-023-10064-y kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 AR 56 2023 1 02 06 55-75 |
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Solving Geophysical Inversion Problems with Intractable Likelihoods: Linearized Gaussian Approximations Versus the Correlated Pseudo-marginal Method Inverse theory (dpeaa)DE-He213 Intractable likelihood (dpeaa)DE-He213 Latent variable model (dpeaa)DE-He213 Hydrogeophysics (dpeaa)DE-He213 |
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Solving Geophysical Inversion Problems with Intractable Likelihoods: Linearized Gaussian Approximations Versus the Correlated Pseudo-marginal Method |
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Abstract A geophysical Bayesian inversion problem may target the posterior distribution of geological or hydrogeological parameters given geophysical data. To account for the scatter in the petrophysical relationship linking the target parameters to the geophysical properties, this study treats the intermediate geophysical properties as latent (unobservable) variables. To perform inversion in such a latent variable model, the intractable likelihood function of the (hydro)geological parameters given the geophysical data needs to be estimated. This can be achieved by approximation with a Gaussian probability density function based on local linearization of the geophysical forward operator, thereby, accounting for the noise in the petrophysical relationship by a corresponding addition to the data covariance matrix. The new approximate method is compared against the general correlated pseudo-marginal method, which estimates the likelihood by Monte Carlo averaging over samples of the latent variable. First, the performances of the two methods are tested on a synthetic test example, in which a multivariate Gaussian porosity field is inferred using crosshole ground-penetrating radar first-arrival travel times. For this example with rather small petrophysical uncertainty, the two methods provide near-identical estimates, while an inversion that ignores petrophysical uncertainty leads to biased estimates. The results of a sensitivity analysis are then used to suggest that the linearized Gaussian approach, while attractive due to its relative computational speed, suffers from a decreasing accuracy with increasing scatter in the petrophysical relationship. The computationally more expensive correlated pseudo-marginal method performs very well even for settings with high petrophysical uncertainty. © The Author(s) 2023 |
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Abstract A geophysical Bayesian inversion problem may target the posterior distribution of geological or hydrogeological parameters given geophysical data. To account for the scatter in the petrophysical relationship linking the target parameters to the geophysical properties, this study treats the intermediate geophysical properties as latent (unobservable) variables. To perform inversion in such a latent variable model, the intractable likelihood function of the (hydro)geological parameters given the geophysical data needs to be estimated. This can be achieved by approximation with a Gaussian probability density function based on local linearization of the geophysical forward operator, thereby, accounting for the noise in the petrophysical relationship by a corresponding addition to the data covariance matrix. The new approximate method is compared against the general correlated pseudo-marginal method, which estimates the likelihood by Monte Carlo averaging over samples of the latent variable. First, the performances of the two methods are tested on a synthetic test example, in which a multivariate Gaussian porosity field is inferred using crosshole ground-penetrating radar first-arrival travel times. For this example with rather small petrophysical uncertainty, the two methods provide near-identical estimates, while an inversion that ignores petrophysical uncertainty leads to biased estimates. The results of a sensitivity analysis are then used to suggest that the linearized Gaussian approach, while attractive due to its relative computational speed, suffers from a decreasing accuracy with increasing scatter in the petrophysical relationship. The computationally more expensive correlated pseudo-marginal method performs very well even for settings with high petrophysical uncertainty. © The Author(s) 2023 |
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Abstract A geophysical Bayesian inversion problem may target the posterior distribution of geological or hydrogeological parameters given geophysical data. To account for the scatter in the petrophysical relationship linking the target parameters to the geophysical properties, this study treats the intermediate geophysical properties as latent (unobservable) variables. To perform inversion in such a latent variable model, the intractable likelihood function of the (hydro)geological parameters given the geophysical data needs to be estimated. This can be achieved by approximation with a Gaussian probability density function based on local linearization of the geophysical forward operator, thereby, accounting for the noise in the petrophysical relationship by a corresponding addition to the data covariance matrix. The new approximate method is compared against the general correlated pseudo-marginal method, which estimates the likelihood by Monte Carlo averaging over samples of the latent variable. First, the performances of the two methods are tested on a synthetic test example, in which a multivariate Gaussian porosity field is inferred using crosshole ground-penetrating radar first-arrival travel times. For this example with rather small petrophysical uncertainty, the two methods provide near-identical estimates, while an inversion that ignores petrophysical uncertainty leads to biased estimates. The results of a sensitivity analysis are then used to suggest that the linearized Gaussian approach, while attractive due to its relative computational speed, suffers from a decreasing accuracy with increasing scatter in the petrophysical relationship. The computationally more expensive correlated pseudo-marginal method performs very well even for settings with high petrophysical uncertainty. © The Author(s) 2023 |
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