Reliability-based design in rock engineering: Application of Bayesian regression methods to rock strength data

Uncertainty is an essential property of rock mechanics and engineering, which is of great significance to excavation, design, and control of rock engineering. In this study, an innovative framework of the reliability-based design was developed for the rock tunnel under uncertainty. The convergence-confinement method is used to characterize the interaction mechanism between the support structure and surrounding rock mass. Artificial bee colony (ABC) was adopted to solve the optimization problem in the reliability-based design. The probabilistic properties of rock strength and failure envelope were obtained based on the triaxial compression test data using the Bayesian method. The reliability of the tunnel and support structure was evaluated based on the abovementioned probabilistic properties of rock strength using the reliability analysis method. A circular tunnel was used to illustrate the developed framework, and the procedure was presented in detail. The time of rockbolt installed, the thickness of the shotcrete, length of rockbolt, circumferential space, and longitudinal space of rockbolt were determined and met the constraints of reliability index. Results show that the developed framework can consider the uncertainty for support design in the tunnel. It provides a good and promising way to support design considering the uncertainty of test data using the reliability-based design.

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A Multiple-Trait Bayesian Variable Selection Regression Method for Integrating Phenotypic Causal Networks in Genome-Wide Association Studies

G3 Genes|Genome|Genetics ◽

10.1534/g3.120.401618 ◽

2020 ◽

Vol 10 (12) ◽

pp. 4439-4448

Author(s):

Zigui Wang ◽

Deborah Chapman ◽

Gota Morota ◽

Hao Cheng

Keyword(s):

Association Studies ◽

Bayesian Variable Selection ◽

Bayesian Regression ◽

Genome Wide Association ◽

Superior Performance ◽

Genome Wide Association Studies ◽

Multiple Trait ◽

Regression Methods ◽

Genome Wide ◽

Causal Structures

Bayesian regression methods that incorporate different mixture priors for marker effects are used in multi-trait genomic prediction. These methods can also be extended to genome-wide association studies (GWAS). In multiple-trait GWAS, incorporating the underlying causal structures among traits is essential for comprehensively understanding the relationship between genotypes and traits of interest. Therefore, we develop a GWAS methodology, SEM-Bayesian alphabet, which, by applying the structural equation model (SEM), can be used to incorporate causal structures into multi-trait Bayesian regression methods. SEM-Bayesian alphabet provides a more comprehensive understanding of the genotype-phenotype mapping than multi-trait GWAS by performing GWAS based on indirect, direct and overall marker effects. The superior performance of SEM-Bayesian alphabet was demonstrated by comparing its GWAS results with other similar multi-trait GWAS methods on real and simulated data. The software tool JWAS offers open-source routines to perform these analyses.

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Multple-trait Bayesian Regression Methods with Mixture Priors for Genomic Prediction

10.1101/102962 ◽

2017 ◽

Author(s):

Hao Cheng ◽

Kadir Kizilkaya ◽

Jian Zeng ◽

Dorian Garrick ◽

Rohan Fernando

Keyword(s):

Multiple Regression ◽

Genomic Prediction ◽

Simulated Data ◽

Software Tool ◽

Real Data ◽

Bayesian Regression ◽

Regression Methods ◽

Data Analyses

ABSTRACTBayesian multiple-regression methods incorporating different mixture priors for marker effects are widely used in genomic prediction. Improvement in prediction accuracies from using those methods, such as BayesB, BayesC and BayesCπ, have been shown in single-trait analyses with both simulated data and real data. These methods have been extended to multi-trait analyses, but only under a specific limited circumstance that assumes a locus affects all the traits or none of them. In this paper, we develop and implement the most general multi-trait BayesCΠ and BayesB methods allowing a broader range of mixture priors. Further, we compare them to single-trait methods and the “restricted” multi-trait formulation using real data. In those data analyses, significant higher prediction accuracies were sometimes observed from these new broad-based multi-trait Bayesian multiple-regression methods. The software tool JWAS offers routines to perform the analyses.

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