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Bayesian maximum entropy

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Journal Article
Published: 04 April 2024
Geochemistry: Exploration, Environment, Analysis (2024) 24 (1): geochem2024-002.
...Bo Zhao; Dongmin Deng; Dehui Zhang; Kun Tang; Panpan Tang; Lin An Abstract In this paper, we present a dual-drive multi-mineral-species anomaly detection system which involves the combined use of Bayesian maximum entropy, a spectral separable module, high-order factor analysis, a geologically...
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Journal Article
Published: 28 October 2013
Canadian Journal of Earth Sciences (2014) 51 (1): 43–55.
... with ordinary Kriging and Bayesian maximum entropy techniques. An estimated point was modified based on the distance from the point to the cluster center. The research considered elevation variations as a secondary variable. A cross-validation technique was used for evaluating the results of mean annual...
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Journal Article
Journal: Geophysics
Published: 01 July 1991
Geophysics (1991) 56 (7): 1003–1014.
... of the Fourier data of the seismic trace within a passband. Uncertainty about the Fourier coefficients can be accounted for by specification of a noise variance, which implicitly is infinite outside the passband. The update with relative entropy inference is justified because of its relationship with Bayesian...
Journal Article
Published: 05 December 2022
Geochemistry: Exploration, Environment, Analysis (2022) 22 (4): geochem2022-029.
... and Bayesian maximum entropy interpolation) have been applied widely in the geosciences (e.g. Krige 1966 ; Christakos 1990 ; Christakos and Serre 2000 ; Cheng 2015 ; Liu et al. 2015 ; Shi et al. 2015 ; Parsa et al. 2017 ; Y. Wang et al. 2017 , H. Wang et al . 2022 a , b ; Ma et al...
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Journal Article
Journal: Geophysics
Published: 05 May 2022
Geophysics (2022) 87 (4): E189–E203.
... ) and hydrogeology (e.g.,  Zhang et al., 2015 ; Tarakanov and Elsheikh, 2020 ). In Bayesian experimental design, the difference between the prior and posterior probability density of model parameters is defined as relative entropy, which represents the information provided by a measurement ( Lindley, 1956 ; Shewry...
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Journal Article
Journal: Geophysics
Published: 01 January 2001
Geophysics (2001) 66 (1): 55–69.
.... The maximum relative entropy approach is, in our opinion, very flexible and computationally much less demanding than the full Bayesian approach, yet it allows the incorporation of probabilistic constraints. Woodbury and Ulrych (1998) and Jacobs and van der Geest (1991) compare the Bayesian and maximum...
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Journal Article
Journal: Geophysics
Published: 20 April 2016
Geophysics (2016) 81 (3): B87–B99.
... maximization (EM) algorithm ( Schlanser et al., 2014 ), which searches the maximum likelihood estimations of the probabilistic model parameters in an iterative way ( Dempster et al., 1977 ). Facies probability conditioned on well-log elastic properties can then be written in a Bayesian framework as P ( F...
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Journal Article
Journal: Geophysics
Published: 24 March 2011
Geophysics (2011) 76 (2): Q1–Q8.
..., ξ is a vector describing the design of the experiment used to observe data d , and ε is the data noise, which may depend on the experimental design ξ . The goal of SED is to optimize ξ before the experiment to obtain maximum information about m after the experiment. A Bayesian statement...
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Journal Article
Journal: The Leading Edge
Published: 01 November 2004
The Leading Edge (2004) 23 (11): 1112–1117.
... , 2000). “Optimal configuration of a seismographic network: a statistical approach” by Rabinowitz and Steinberg ( SSA Bulletin , 1990). “Maximum entropy sampling and optimal Bayesian experimental design” by Sebastiani and Wynn ( Journal of the Royal Statistical Society B , Part 1, 2000). “A mathematical...
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Journal Article
Journal: Geophysics
Published: 17 October 2000
Geophysics (2001) 66 (2): 389–397.
... to make a somewhat more objective choice of priors by relying on theoretical considerations such as maximum entropy ( Jaynes, 1982 ) or transformation invariance ( Jaynes, 1968 ; Dawid, 1983 ), or by somehow using observations to estimate a prior. This latter approach is the empirical Bayes mentioned...
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Journal Article
Journal: Interpretation
Published: 21 June 2016
Interpretation (2016) 4 (3): SM1–SM16.
... . In almost all practical cases, an analytical calculation of the denominator in equation  2 is not directly possible due to the intractability of the multidimensional space. This difficulty is partly responsible for the lack of wider use of Bayesian methods. In this paper, we apply the commonly used maximum...
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Journal Article
Journal: Geophysics
Published: 07 January 2021
Geophysics (2021) 86 (1): M17–M28.
... represents the proportion of each facies class, and the weighted success rate and entropy indices provide a more target-oriented evaluation. We used Bayesian classification to assign facies labels. Use of a naïve Bayes classifier casts the classification into a probabilistic framework. It provides...
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Journal Article
Journal: Geophysics
Published: 16 November 2015
Geophysics (2016) 81 (1): V7–V16.
...Kenji Nose-Filho; André K. Takahata; Renato Lopes; João M. T. Romano ABSTRACT We have addressed blind deconvolution in a multichannel framework. Recently, a robust solution to this problem based on a Bayesian approach called sparse multichannel blind deconvolution (SMBD) was proposed...
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Journal Article
Journal: Geophysics
Published: 06 December 2022
Geophysics (2023) 88 (1): G1–G18.
... with the ground truth value due to the less restricted likelihood function chosen. This allows us to keep the information of the prior knowledge and prevent it from reducing back to a maximum likelihood problem. This is the fundamental difference between Bayesian inference and minimizing the data misfit...
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Journal Article
Published: 01 June 2001
Environmental Geosciences (2001) 8 (2): 140–143.
... in the doctrine of chances . Phil Trans Roy Soc , 53 , 370 – 418 . Jaynes , E. T. ( 1978 ). Where do we stand on maximum entropy? In R. D. Levine and M. Tribus (Eds.), The maximum entropy formalism (pp. 15 – 118 ). Cambridge, MA : MIT Press . Lerche , I. , and MacKay...
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Journal Article
Journal: Geophysics
Published: 01 June 2020
Geophysics (2020) 85 (4): MR213–MR233.
... discriminated properties as seen in the log data, high entropy within some layers indicates the presence of mix brine-sand and shale lithology that is not well discriminated. Figure  14a shows the facies map with maximum marginal distributions in each model cell for the three inverted facies: shale, brine-sand...
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Journal Article
Journal: Geophysics
Published: 27 June 2022
Geophysics (2022) 87 (4): IM157–IM176.
..., they provide no means to interpret the uncertainty of their predictions. We compare three different approaches for obtaining probabilistic models based on convolutional neural networks in a Bayesian formalism, namely, deep ensembles, concrete dropout, and stochastic weight averaging Gaussian (SWAG...
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Journal Article
Journal: The Leading Edge
Published: 01 February 2020
The Leading Edge (2020) 39 (2): 102–109.
... support vector machine and deep learning : Geophysical Prospecting , 67 , no. 4 , 1040 – 1054 , https://doi.org/10.1111/1365-2478.12682 . Pendrel , J. , and H. J. Schouten , 2019 , Entropy QC for Bayesian facies estimations : 89th Annual International Meeting , SEG, Expanded...
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Journal Article
Journal: Geophysics
Published: 24 October 2018
Geophysics (2018) 83 (6): V345–V357.
... and the nature of the signal of interest ( Campisi and Egiazarian, 2017 ). Some of the main Bayesian methods in blind deconvolution are maximum a posteriori and maximum likelihood methods ( Lagendijk et al., 1988 ; Katsaggelos, 1989 ; Katsaggelos et al., 1991 ; You and Kaveh, 1996 ), iterated conditional...
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Journal Article
Journal: Geophysics
Published: 29 January 2016
Geophysics (2016) 81 (1): 1JF–3JF.
.... Zou et al. use the maximum entropy method to invert the nuclear magnetic resonance echo data and propose a simple and effective method for solving the maximum entropy function. Lee et al. describe how the dipole tool commonly used in shear-wave logging can significantly affect the dispersion...