Inference of the Transition Matrix in Convolved Hidden Markov Models and the Generalized Baum–Welch Algorithm

Lindberg, David Volent; Omre, Henning

doi:10.1109/tgrs.2015.2440415

Cited by 24 publications

(11 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Assessment of aMAP k requires the use of the recursive Viterbi algorithm [31]. We refer to [20] for a discussion of model parameter estimation in a convolved hidden Markov model. The correct posterior model p κ| d is assessed by an independent proposal MCMC MH algorithm [26] using p (k) κ| d as proposal distribution.…”

Section: Assessment Of Posterior Modelmentioning

confidence: 99%

Bayesian Inversion of Convolved Hidden Markov Models With Applications in Reservoir Prediction

Fjeldstad

Omre

2020

IEEE Trans. Geosci. Remote Sensing

Self Cite

View full text Add to dashboard Cite

Efficient assessment of convolved hidden Markov models is discussed. The bottom-layer is defined as an unobservable categorical first-order Markov chain, while the middle-layer is assumed to be a Gaussian spatial variable conditional on the bottom-layer. Hence, this layer appear as a Gaussian mixture spatial variable unconditionally. We observe the top-layer as a convolution of the middle-layer with Gaussian errors. Focus is on assessment of the categorical and Gaussian mixture variables given the observations, and we operate in a Bayesian inversion framework. The model is defined to make inversion of subsurface seismic AVO data into lithology/fluid classes and to assess the associated elastic material properties. Due to the spatial coupling in the likelihood functions, evaluation of the posterior normalizing constant is computationally demanding, and brute-force, singlesite updating Markov chain Monte Carlo algorithms converges far too slow to be useful. We construct two classes of approximate posterior models which we assess analytically and efficiently using the recursive Forward-Backward algorithm. These approximate posterior densities are used as proposal densities in an independent proposal Markov chain Monte Carlo algorithm, to assess the correct posterior model. A set of synthetic realistic examples are presented. The proposed approximations provides efficient proposal densities which results in acceptance probabilities in the range 0.10-0.50 in the Markov chain Monte Carlo algorithm. A case study of lithology/fluid seismic inversion is presented. The lithology/fluid classes and the elastic material properties can be reliably predicted. * torstein.fjeldstad@ntnu.no 1 arXiv:1710.06613v1 [physics.geo-ph]

show abstract

Section: Assessment Of Posterior Modelmentioning

confidence: 99%

Bayesian Inversion of Convolved Hidden Markov Models With Applications in Reservoir Prediction

Fjeldstad

Omre

2020

IEEE Trans. Geosci. Remote Sensing

Self Cite

View full text Add to dashboard Cite

show abstract

“…The inversion formulation adopted in this thesis is known as Convolved Hidden Markov Model (1,10). This tool will allow to quantify the probability of hydrocarbon reservoir in different points of the subsurface.…”

Section: Objectives Of This Thesismentioning

confidence: 99%

“…As a consequence the output seismic profile has smaller length than the input elastic and facies profiles, as illustrated in figure 3.4. As demonstrated in section B.5, the seismic conditional probability given the facies profile is computed by: (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15) In order to estimate the inverse conditional probability p(π|s) (also known as posterior probability), the Bayes theorem was used:…”

Section: Seismic Inversion To Faciesmentioning

confidence: 99%

“…Equation B-23 defines the signal-to-noise ratio. In order to compute this ratio, one needs an estimate of Σ XX , which comes from the approximate Gaussian covariance matrix Σ * (equation [5][6][7][8][9][10][11][12][13].…”

Section: • Transition Matrixmentioning

confidence: 99%

“…But for multidimensional problems, or complex combinatorial problems, the sampling itself might be hard to be implemented, or even, the probability distribution is known up to an unknown normalizing constant (such as in equation [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In these cases, one uses the technique known as Markov Chain Monte Carlo (MCMC), which instead of sampling independent identically distributed samples of the proposed distribution, uses a Markov Chain, whose stationary distribution is the required distribution.…”

Section: E1 Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Seismic to Facies Inversion Using Convolved Hidden Markov Model

TALARICO¹

View full text Add to dashboard Cite

Adjustable loads control and stochastic stability analysis for multi-energy generation system based on Markov model

Zhai

Sun

Cui

et al. 2019

Neural Comput & Applic

View full text Add to dashboard Cite

Inference of the Transition Matrix in Convolved Hidden Markov Models and the Generalized Baum–Welch Algorithm

Cited by 24 publications

References 18 publications

Bayesian Inversion of Convolved Hidden Markov Models With Applications in Reservoir Prediction

Bayesian Inversion of Convolved Hidden Markov Models With Applications in Reservoir Prediction

Seismic to Facies Inversion Using Convolved Hidden Markov Model

Adjustable loads control and stochastic stability analysis for multi-energy generation system based on Markov model

Contact Info

Product

Resources

About