Bayesian evidence computation for model selection in non-linear geoacoustic inference problems

Dettmer, Jan; Dosso, Stan E.; Osler, John C.

doi:10.1121/1.3506345

Cited by 35 publications

(28 citation statements)

References 43 publications

(35 reference statements)

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“…Gelfand and Dey (1994) suggest that the integral of the posterior distribution can be estimated via numerical integration using, for instance, Monte Carlo methods ( Hammersley and Handscomb, 1964 ), asymptotic solutions (e.g., Bayesian information criterion, BIC) ( Schwarz et al, 1978 ) or Laplace's method ( De Bruijn, 1970 ). In the field of geophysics, BIC ( Dettmer et al, 2009 ), annealed importance sampling ( Dettmer et al, 2010 ) and the deviance information criterion, DIC, ( Spiegelhalter et al, 2002;Steininger et al, 2014 ) have been used for calculation of the evidence.…”

Section: Introductionmentioning

confidence: 99%

Bayesian model selection in hydrogeophysics: Application to conceptual subsurface models of the South Oyster Bacterial Transport Site, Virginia, USA

Brunetti

Linde

Vrugt

2017

Advances in Water Resources

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a b s t r a c tGeophysical data can help to discriminate among multiple competing subsurface hypotheses (conceptual models). Here, we explore the merits of Bayesian model selection in hydrogeophysics using crosshole ground-penetrating radar data from the South Oyster Bacterial Transport Site in Virginia, USA. Implementation of Bayesian model selection requires computation of the marginal likelihood of the measured data, or evidence, for each conceptual model being used. In this paper, we compare three different evidence estimators, including (1) the brute force Monte Carlo method, (2) the Laplace-Metropolis method, and (3) the numerical integration method proposed by Volpi et al. (2016). The three types of subsurface models that we consider differ in their treatment of the porosity distribution and use (a) horizontal layering with fixed layer thicknesses, (b) vertical layering with fixed layer thicknesses and (c) a multi-Gaussian field. Our results demonstrate that all three estimators provide equivalent results in low parameter dimensions, yet in higher dimensions the brute force Monte Carlo method is inefficient. The isotropic multi-Gaussian model is most supported by the travel time data with Bayes factors that are larger than 10 100 compared to conceptual models that assume horizontal or vertical layering of the porosity field.

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Section: Introductionmentioning

confidence: 99%

Bayesian model selection in hydrogeophysics: Application to conceptual subsurface models of the South Oyster Bacterial Transport Site, Virginia, USA

Brunetti

Linde

Vrugt

2017

Advances in Water Resources

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“…Williams et al, 2006;Dietzel and Reichert, 2012;Del Giudice et al, 2015) and objective selection of the "best" model (e.g. Dettmer et al, 2010;Del Giudice et al, 2015) can be added to this list. The large potential of Bayesian methods for the CWE community is however contrasted by their limited application.…”

Section: Introductionmentioning

confidence: 99%

Employing statistical model emulation as a surrogate for CFD

Moonen

Allegrini

2015

Environmental Modelling & Software

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“…10 Model parametrization (e.g., the number of seabed layers) plays a fundamental role in obtaining meaningful environmental uncertainty estimates. 4,[10][11][12] The Bayesian information criterion has been applied to address model parametrization selection 11 but represents a point estimate [computed at the maximum a posteriori (MAP) estimate] which may not adequately represent the model space. In a more rigorous and quantitative approach, Bayesian evidence (the likelihood of the model gives the measured data) can be computed 4,12 using methods such as annealed importance sampling 13 (AIS).…”

Section: Introductionmentioning

confidence: 99%

Sequential trans-dimensional Monte Carlo for range-dependent geoacoustic inversion

Dettmer

Dosso

Holland

2011

The Journal of the Acoustical Society of America

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This paper develops a sequential trans-dimensional Monte Carlo algorithm for geoacoustic inversion in a strongly range-dependent environment. The algorithm applies advanced Markov chain Monte Carlo methods in combination with sequential techniques (particle filters) to carry out geoacoustic inversions for consecutive data sets acquired along a track. Changes in model parametrization along the track (e.g., number of sediment layers) are accounted for with trans-dimensional partition modeling, which intrinsically determines the amount of structure supported by the data information content. Challenging issues of rapid environmental change between consecutive data sets and high information content (peaked likelihood) are addressed by bridging distributions implemented using annealed importance sampling. This provides an efficient method to locate high-likelihood regions for new data which are distant and ∕ or disjoint from previous high-likelihood regions. The algorithm is applied to simulated reflection-coefficient data along a track, such as can be collected using a towed array close to the seabed. The simulated environment varies rapidly along the track, with changes in the number of layers, layer thicknesses, and geoacoustic parameters within layers. In addition, the seabed contains a geologic fault, where all layers are offset abruptly, and an erosional channel. Changes in noise level are also considered.

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Bayesian evidence computation for model selection in non-linear geoacoustic inference problems

Cited by 35 publications

References 43 publications

Bayesian model selection in hydrogeophysics: Application to conceptual subsurface models of the South Oyster Bacterial Transport Site, Virginia, USA

Bayesian model selection in hydrogeophysics: Application to conceptual subsurface models of the South Oyster Bacterial Transport Site, Virginia, USA

Employing statistical model emulation as a surrogate for CFD

Sequential trans-dimensional Monte Carlo for range-dependent geoacoustic inversion

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