A Bayesian inference framework for fault slip distributions based on ensemble modeling of the uncertainty of underground structure - With a focus on uncertain fault dip

Summary The model prediction errors that originate from the uncertainty of underground structure is often a major contributor of the errors between the data and the model predictions in fault slip estimation using geodetic or seismic waveform data. However, most studies on slip inversions either neglect the model prediction errors or do not distinguish them from observation errors. Several methods that explicitly incorporated the model prediction errors in slip estimation, which has been proposed in the past decade, commonly assumed a Gaussian distribution for the stochastic property of the model prediction errors to simplify the formulation. Moreover, the information on both the slip distribution and the underground structure is expected to be successfully extracted from the data by incorporating the stochastic property of the model prediction errors. In this study, we propose a novel flexible Bayesian inference framework for estimating fault slips that can accurately incorporate non-Gaussian model prediction errors. This method considers the uncertainty of the underground structure, including fault geometry, based on the ensemble modeling of the uncertainty of Green’s functions. Furthermore, the framework allows the estimation of the posterior probability density function (PDF) of the parameters of the underground structure, by calculating the likelihood of each sample in the ensemble. We performed numerical experiments for estimating the slip deficit rate (SDR) distribution on a 2D thrust fault using synthetic data of surface displacement rates, which is the simplest problem setting that can essentially demonstrates the fundamental idea and validate the advantage of the proposed method. In the experiments, the dip angle of the fault plane was the parameter used to characterize the underground structure. The proposed method succeeded in estimating a posterior PDF of SDR that is consistent with the true one, despite the uncertain and inaccurate information of the dip angle. In addition, the method could estimate a posterior PDF of the dip angle that has a strong peak near the true angle. In contrast, the estimation results obtained using a conventional approach, which introduces regularization based on smoothing constraints and does not explicitly distinguish the prediction and observation errors, included a significant amount of bias, which was not noticed in the results obtained using the proposed method. The estimation results obtained using different settings of the parameters suggested that inaccurate prior information of the underground structure with a small variance possibly results in significant bias in the estimated PDFs, particularly the posterior PDFs for SDR, those for the underground structure, and the posterior predicted PDF of the displacement rates. The distribution shapes of the model prediction errors for the representative model parameters in certain observation points are significantly asymmetric with large absolute values of the sample skewness, suggesting that they would not be well-modeled by Gaussian approximations.

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Bayesian inference for fault slip distributions based on ensemble modeling of the uncertainty of underground structure

10.31223/osf.io/2czpx ◽

2020 ◽

Author(s):

Ryoichiro Agata ◽

Amato Kasahara ◽

Yuji Yagi

Keyword(s):

Bayesian Inference ◽

Underground Structure ◽

Fault Slip ◽

Ensemble Modeling

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Learning Model Discrepancy of an Electric Motor with Bayesian Inference

Proceedings ◽

10.3390/proceedings2019033011 ◽

2019 ◽

Vol 33 (1) ◽

pp. 11

Author(s):

David N. John ◽

Michael Schick ◽

Vincent Heuveline

Keyword(s):

Bayesian Inference ◽

Electric Motor ◽

Computational Models ◽

Measurement Data ◽

Simulation Models ◽

Model Parameters ◽

Main Challenge ◽

Model Discrepancy ◽

Bayesian Inference Framework ◽

Computational Modeling And Simulation

Uncertainty Quantification (UQ) is highly requested in computational modeling and simulation, especially in an industrial context. With the continuous evolution of modern complex systems demands on quality and reliability of simulation models increase. A main challenge is related to the fact that the considered computational models are rarely able to represent the true physics perfectly and demonstrate a discrepancy compared to measurement data. Further, an accurate knowledge of considered model parameters is usually not available. e.g., fluctuations in manufacturing processes of hardware components or noise in sensors introduce uncertainties which must be quantified in an appropriate way. Mathematically, such UQ tasks are posed as inverse problems, requiring efficient methods to solve. This work investigates the influence of model discrepancies onto the calibration of physical model parameters and further considers a Bayesian inference framework including an attempt to correct for model discrepancy. A polynomial expansion is used to approximate and learn model discrepancy. This work extends by discussion and specification of a guideline on how to define the model discrepancy term complexity, based on the available data. Application to an electric motor model with synthetic measurements illustrates the importance and promising perspective of the method.

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Comparing two sequential Monte Carlo samplers for exact and approximate Bayesian inference on biological models

Journal of The Royal Society Interface ◽

10.1098/rsif.2017.0340 ◽

2017 ◽

Vol 14 (134) ◽

pp. 20170340 ◽

Cited By ~ 6

Author(s):

Aidan C. Daly ◽

Jonathan Cooper ◽

David J. Gavaghan ◽

Chris Holmes

Keyword(s):

Bayesian Inference ◽

Bayesian Methods ◽

Sequential Monte Carlo ◽

Model Parameters ◽

Biological Models ◽

Exact Inference ◽

Modelling Studies ◽

Approximate Bayesian ◽

Approximate Bayesian Inference ◽

Abc Methods

Bayesian methods are advantageous for biological modelling studies due to their ability to quantify and characterize posterior variability in model parameters. When Bayesian methods cannot be applied, due either to non-determinism in the model or limitations on system observability, approximate Bayesian computation (ABC) methods can be used to similar effect, despite producing inflated estimates of the true posterior variance. Owing to generally differing application domains, there are few studies comparing Bayesian and ABC methods, and thus there is little understanding of the properties and magnitude of this uncertainty inflation. To address this problem, we present two popular strategies for ABC sampling that we have adapted to perform exact Bayesian inference, and compare them on several model problems. We find that one sampler was impractical for exact inference due to its sensitivity to a key normalizing constant, and additionally highlight sensitivities of both samplers to various algorithmic parameters and model conditions. We conclude with a study of the O'Hara–Rudy cardiac action potential model to quantify the uncertainty amplification resulting from employing ABC using a set of clinically relevant biomarkers. We hope that this work serves to guide the implementation and comparative assessment of Bayesian and ABC sampling techniques in biological models.

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Explaining Neural Networks Using Attentive Knowledge Distillation

Sensors ◽

10.3390/s21041280 ◽

2021 ◽

Vol 21 (4) ◽

pp. 1280

Author(s):

Hyeonseok Lee ◽

Sungchan Kim

Keyword(s):

Neural Networks ◽

Model Prediction ◽

Saliency Map ◽

Model Parameters ◽

Learning Capability ◽

Fine Grained ◽

Network Layers ◽

Saliency Maps ◽

Novel Approach ◽

Knowledge Distillation

Explaining the prediction of deep neural networks makes the networks more understandable and trusted, leading to their use in various mission critical tasks. Recent progress in the learning capability of networks has primarily been due to the enormous number of model parameters, so that it is usually hard to interpret their operations, as opposed to classical white-box models. For this purpose, generating saliency maps is a popular approach to identify the important input features used for the model prediction. Existing explanation methods typically only use the output of the last convolution layer of the model to generate a saliency map, lacking the information included in intermediate layers. Thus, the corresponding explanations are coarse and result in limited accuracy. Although the accuracy can be improved by iteratively developing a saliency map, this is too time-consuming and is thus impractical. To address these problems, we proposed a novel approach to explain the model prediction by developing an attentive surrogate network using the knowledge distillation. The surrogate network aims to generate a fine-grained saliency map corresponding to the model prediction using meaningful regional information presented over all network layers. Experiments demonstrated that the saliency maps are the result of spatially attentive features learned from the distillation. Thus, they are useful for fine-grained classification tasks. Moreover, the proposed method runs at the rate of 24.3 frames per second, which is much faster than the existing methods by orders of magnitude.

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Bayesian Inference of Species Trees using Diffusion Models

Systematic Biology ◽

10.1093/sysbio/syaa051 ◽

2020 ◽

Vol 70 (1) ◽

pp. 145-161 ◽

Cited By ~ 1

Author(s):

Marnus Stoltz ◽

Boris Baeumer ◽

Remco Bouckaert ◽

Colin Fox ◽

Gordon Hiscott ◽

...

Keyword(s):

Bayesian Inference ◽

Numerical Algorithms ◽

Diffusion Models ◽

Model Parameters ◽

Data Sets ◽

Species Trees ◽

Computationally Efficient ◽

Data Set ◽

Snp Data ◽

Binary Markers

Abstract We describe a new and computationally efficient Bayesian methodology for inferring species trees and demographics from unlinked binary markers. Likelihood calculations are carried out using diffusion models of allele frequency dynamics combined with novel numerical algorithms. The diffusion approach allows for analysis of data sets containing hundreds or thousands of individuals. The method, which we call Snapper, has been implemented as part of the BEAST2 package. We conducted simulation experiments to assess numerical error, computational requirements, and accuracy recovering known model parameters. A reanalysis of soybean SNP data demonstrates that the models implemented in Snapp and Snapper can be difficult to distinguish in practice, a characteristic which we tested with further simulations. We demonstrate the scale of analysis possible using a SNP data set sampled from 399 fresh water turtles in 41 populations. [Bayesian inference; diffusion models; multi-species coalescent; SNP data; species trees; spectral methods.]

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Uncertainty analysis in model parameters regionalization: a case study involving the SWAT model in Mediterranean catchments (Southern France)

Hydrology and Earth System Sciences ◽

10.5194/hess-18-2393-2014 ◽

2014 ◽

Vol 18 (6) ◽

pp. 2393-2413 ◽

Cited By ~ 34

Author(s):

H. Sellami ◽

I. La Jeunesse ◽

S. Benabdallah ◽

N. Baghdadi ◽

M. Vanclooster

Keyword(s):

Model Prediction ◽

Hydrological Model ◽

Swat Model ◽

Behavioral Model ◽

Model Parameters ◽

Ungauged Catchments ◽

Southern France ◽

Model Parameter ◽

Ungauged Catchment ◽

Prediction Uncertainty

Abstract. In this study a method for propagating the hydrological model uncertainty in discharge predictions of ungauged Mediterranean catchments using a model parameter regionalization approach is presented. The method is developed and tested for the Thau catchment located in Southern France using the SWAT hydrological model. Regionalization of model parameters, based on physical similarity measured between gauged and ungauged catchment attributes, is a popular methodology for discharge prediction in ungauged basins, but it is often confronted with an arbitrary criterion for selecting the "behavioral" model parameter sets (Mps) at the gauged catchment. A more objective method is provided in this paper where the transferrable Mps are selected based on the similarity between the donor and the receptor catchments. In addition, the method allows propagating the modeling uncertainty while transferring the Mps to the ungauged catchments. Results indicate that physically similar catchments located within the same geographic and climatic region may exhibit similar hydrological behavior and can also be affected by similar model prediction uncertainty. Furthermore, the results suggest that model prediction uncertainty at the ungauged catchment increases as the dissimilarity between the donor and the receptor catchments increases. The methodology presented in this paper can be replicated and used in regionalization of any hydrological model parameters for estimating streamflow at ungauged catchment.

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Optimization-driven identification of genetic perturbations accelerates the convergence of model parameters in ensemble modeling of metabolic networks

Biotechnology Journal ◽

10.1002/biot.201200270 ◽

2013 ◽

Vol 8 (9) ◽

pp. 1090-1104 ◽

Cited By ~ 19

Author(s):

Ali R. Zomorrodi ◽

Jimmy G. Lafontaine Rivera ◽

James C. Liao ◽

Costas D. Maranas

Keyword(s):

Metabolic Networks ◽

Model Parameters ◽

Ensemble Modeling ◽

Genetic Perturbations

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Modeling the crashes count using finite mixture models

Muthanna Journal of Pure Science ◽

10.52113/2/07.01.2020/13-27 ◽

2019 ◽

Vol 7 (1) ◽

pp. 13-27

Author(s):

Safaa K. Kadhem ◽

Sadeq A. Kadhim

Keyword(s):

Bayesian Inference ◽

Mixture Models ◽

Gibbs Sampler ◽

Simulation Study ◽

Finite Mixture Models ◽

Synthetic Data ◽

Finite Mixture Model ◽

Finite Mixture ◽

Model Parameters ◽

Mcmc Method

"This paper aims at the modeling the crashes count in Al Muthanna governance using finite mixture model. We use one of the most common MCMC method which is called the Gibbs sampler to implement the Bayesian inference for estimating the model parameters. We perform a simulation study, based on synthetic data, to check the ability of the sampler to find the best estimates of the model. We use the two well-known criteria, which are the AIC and BIC, to determine the best model fitted to the data. Finally, we apply our sampler to model the crashes count in Al Muthanna governance.

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