Application of the transitional Markov chain Monte Carlo algorithm to probabilistic site characterization

Ching, Jianye; Wang, Jiun-Shiang

doi:10.1016/j.enggeo.2015.10.015

Cited by 85 publications

(39 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Therefore, 2000 N s total samples were generated in the enhanced TMCMC simulation. According to previous results, the total number of stages for different model class selections was not always the same.…”

Section: Selection Of Sand Modelsmentioning

confidence: 85%

“…Consequently, p(θ) 0 equals the prior distribution p(θ) for j = 0, and p(θ) m is the posterior distribution p(θ|D) for j = m. The details of the original TMCMC method, with its MATLAB code, can be found in Ching and Wang. 67 In the original TMCMC, the new samples are generated from a normal distribution with the mean and standard error calculated from the samples of last iteration. However, some observations have indicated that the inappropriate mean value and standard deviation error can result in the estimated posteriors tending to fall into local convergence.…”

Section: Enhancement Of Tmcmc Methodsmentioning

confidence: 99%

“…The details of the original TMCMC method, with its MATLAB code, can be found in Ching and Wang . In the original TMCMC, the new samples are generated from a normal distribution with the mean and standard error calculated from the samples of last iteration.…”

Section: Model Selection Approach and Generalization Ability Evaluationmentioning

confidence: 99%

See 2 more Smart Citations

Bayesian model selection for sand with generalization ability evaluation

Jin

Yin

Zhou

et al. 2019

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

Summary Current studies have focused on selecting constitutive models using optimization methods or selecting simple formulas or models using Bayesian methods. In contrast, this paper deals with the challenge to propose an effective Bayesian‐based selection method for advanced soil models accounting for the soil uncertainty. Four representative critical state‐based advanced sand models are chosen as database of constitutive model. Triaxial tests on Hostun sand are selected as training and testing data. The Bayesian method is enhanced based on transitional Markov chain Monte Carlo method, whereby the generalization ability for each model is simultaneously evaluated, for the model selection. The most plausible/suitable model in terms of predictive ability, generalization ability, and model complexity is selected using training data. The performance of the method is then validated by testing data. Finally, a series of drained triaxial tests on Karlsruhe sand is used for further evaluating the performance.

show abstract

Section: Selection Of Sand Modelsmentioning

confidence: 85%

Section: Enhancement Of Tmcmc Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Bayesian model selection for sand with generalization ability evaluation

Jin

Yin

Zhou

et al. 2019

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

show abstract

“…Some examples include the Annealed Importance Sampling [5], the Adaptive Metropolis-Hastings method [6], and the Iterated Batch Importance Sampling Algorithm [7], etc. Among them, [8] proposed the Transitional Markov Chain Monte Carlo (TMCMC) method with applications on Bayesian inference of structural dynamics problems, as well as other engineering applications [9]. The fundamental concept of TMCMC is to sequentially update samples drawn from prior distribution (usually easy to sample from) to the posterior distribution in the Bayesian framework.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Annealed Sequential Importance Sampling: An Unbiased Version of Transitional Markov Chain Monte Carlo

Angelikopoulos

Papadimitriou

et al. 2017

ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering

View full text Add to dashboard Cite

The transitional Markov chain Monte Carlo (TMCMC) is one of the efficient algorithms for performing Markov chain Monte Carlo (MCMC) in the context of Bayesian uncertainty quantification in parallel computing architectures. However, the features that are associated with its efficient sampling are also responsible for its introducing of bias in the sampling. We demonstrate that the Markov chains of each subsample in TMCMC may result in uneven chain lengths that distort the intermediate target distributions and introduce bias accumulation in each stage of the TMCMC algorithm. We remedy this drawback of TMCMC by proposing uniform chain lengths, with or without burn-in, so that the algorithm emphasizes sequential importance sampling (SIS) over MCMC. The proposed Bayesian annealed sequential importance sampling (BASIS) removes the bias of the original TMCMC and at the same time increases its parallel efficiency. We demonstrate the advantages and drawbacks of BASIS in modeling of bridge dynamics using finite elements and a disk-wall collision using discrete element methods.

show abstract

“…Due to the fact that ground motion prediction always associates significant uncertainty, Bayesian learning framework (Bishop, ; Beck, ) is introduced in the study to provide a rigorous solution for uncertainty quantification for both parametric level (learning within a model class;) (Papadimitriou and Papadimitriou, ; Sun et al., ; Yuen and Kuok, ) and model class level (learning with a set of model classes;) (Adeli and Panakkat, ; Ching and Wang, ; Cheung and Beck, ; Huang et al., ; Kuok et al., ; Yuen and Mu, ). The framework has been developed and applied to different areas such as earthquake engineering (Zhou and Adeli, ; Sirca and Adeli, ; Panakkat and Adeli, , ), instrument defect detection (Castillo et al., ; Wang et al., ; Yin et al., ), structural dynamics (Ching et al., ; Lam et al., ; Lei et al., ; Lei et al., ; Sun and Betti, ), structural identification, and health monitoring (Jiang et al., ; Simoen et al., ; Spackova and Straub, ; Yuen and Katafygiotis, ).…”

Section: Introductionmentioning

confidence: 99%

Ground Motion Prediction Equation Development by Heterogeneous Bayesian Learning

Yuen

2016

Computer aided Civil Eng

View full text Add to dashboard Cite

In ground motion prediction, the key is to develop a suitable and reliable GMPE (ground motion prediction equation) characterizing the ground motion pattern of the target seismic region. There are two critical goals encountered in GMPE development. Proposing a suitable predictive formula applicable to target seismic region has attracted much of the attention in previous studies. On the other hand, dependence between prediction–error variance and ground motion data has been observed and the study on this kind of heterogeneous relation becomes an important task yet to be explored. In this article, a novel HEteRogeneous BAyesian Learning (HERBAL) approach is proposed for achieving these two goals simultaneously. The homogeneity assumption on error in the traditional learning approach is relaxed, so the proposed approach is applicable for more general heterogeneous cases. With the generalization made on the traditional Bayesian learning by embedding the derived closed form expression for error variance parameter optimization component into the hyperparameter optimization of ARD (automatic relevance determination) prior, the proposed learning approach is capable of performing continuous model training on a prescribed predictive formula with unknown error pattern. A database of strong ground motion records in the Tangshan region of China is obtained for the analysis. It is shown that the trained optimal model class by the proposed approach is promising as that, the trained optimal model class retains model simplicity of the predictive formula with capability on both robustness enhancement ground motion prediction and precise determination of the error pattern.

show abstract

Application of the transitional Markov chain Monte Carlo algorithm to probabilistic site characterization

Cited by 85 publications

References 33 publications

Bayesian model selection for sand with generalization ability evaluation

Bayesian model selection for sand with generalization ability evaluation

Bayesian Annealed Sequential Importance Sampling: An Unbiased Version of Transitional Markov Chain Monte Carlo

Ground Motion Prediction Equation Development by Heterogeneous Bayesian Learning

Contact Info

Product

Resources

About