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Recognizing risk factors associated with crash frequency on rural four lane highways
Published in Sandra Erkens, Xueyan Liu, Kumar Anupam, Yiqiu Tan, Functional Pavement Design, 2016
C. Naveen Kumar, M. Parida, S.S. Jain
Full Bayesian framework was implemented for modeling and inference. The parameter estimation and inference can be obtained by means of Markov Chain Monte Carlo (MCMC) and software such as WinBUGS. As the Bayesian formulation requires priors for all unknown parameters, non-informative normal priors for β’s and gamma/lognormal priors for error terms were adopted.
Bayesian Network–Based Fault Diagnostic System for Nuclear Power Plant Assets
Published in Nuclear Technology, 2023
Xingang Zhao, Xinyan Wang, Michael W. Golay
Sampling-based tools, the second BN software category, handle the implementation of Bayesian graphical models (BGMs), which relax the assumption of BNs that all variable nodes are categorically distributed. In other words, BNs are a special branch of BGMs. The variables in BGMs can have arbitrary (discrete or continuous) probability distributions, and the parameters are explicitly modeled as nodes. Because of their generality, BGMs are analytically untraceable, and sampling-based inference algorithms such as those of MCMC are used to approximate the joint distribution. One of the first MCMC samplers for BGMs is the WinBUGS software package; its open-source version is called OpenBUGS. A popular alternative to WinBUGS is the JAGS sampler. Packages exist that each provide an interface to JAGS, such as pyjags in Python and rjags in R. Additionally, open-source library options that include MCMC functionality are available, such as the Python module pymc3 and the C++ module mcmclib.
Examining two-wheelers' overtaking behavior and lateral distance choices at a shared roadway facility
Published in Journal of Transportation Safety & Security, 2020
Yanyong Guo, Tarek Sayed, Mohamed H. Zaki
The Bayesian analysis software WinBUGS (Lunn, Thomas, Best, & Spiegelhalter, 2000) is used as the modeling platform for model estimation. The Markov Chain Monte Carlo (MCMC) technique is used to approximate the probability distribution (i.e., the posterior Mean and Standard Deviation) of the parameters. Two independent Markov chains for each of the parameters run for 20,000 iterations. The first 10,000 interactions were used for monitoring convergence and then excluded as a burn-in sample. The remaining interactions were adopted for parameters estimation. To check convergence, two parallel chains with various starting values were tracked so that full coverage of the sample space was ensured. Brooks–Gelman–Rubin (BGR) statistic was also checked, where convergence occurs if the value of the BGR statistic is less than 1.2 (El-Basyouny & Sayed, 2009). Moreover, convergence was checked by visually inspecting the MCMC trace plots of the model parameters.
Evaluating how right-turn treatments affect right-turn-on-red conflicts at signalized intersections
Published in Journal of Transportation Safety & Security, 2020
Yanyong Guo, Pan Liu, Yao Wu, Jingxu Chen
The Bayesian analysis software WinBUGS (Spiegelhalter, Thomas, Best, & Lunn, 2003) is used as the modeling platform for model estimation. The MCMC technique is used to approximate the probability distribution (i.e., the posterior Mean and Standard Deviation) of the model parameters. Two independent Markov chains for each of the parameters run for 20,000 iterations. The first 10,000 interactions are used for monitoring convergence and then excluded as a burn-in sample. The remaining interactions are adopted for parameters estimation. To check convergence, two parallel chains with various starting values are tracked so that full coverage of the sample space is ensured. Brooks-Gelman-Rubin (BGR) statistic is also checked, where convergence occurs if the value of the BGR statistic is less than 1.2 (El-Basyouny & Sayed, 2009). Moreover, convergence was checked by visually inspecting the MCMC trace plots of the model parameters.