China
Africa
Explore chapters and articles related to this topic
Bayesian economic analyses of including reclaimed asphalt pavements in flexible pavement rehabilitation
Published in John Harvey, Imad L. Al-Qadi, Hasan Ozer, Gerardo Flintsch, Pavement, Roadway, and Bridge Life Cycle Assessment 2020, 2020
Hongren Gong, Miaomiao Zhang, Wei Hu, Baoshan Huang*
Equation (2) is the Bayesian equation, the denominator PD is the evidence that can be determined through marginalizing over the prior distribution of the parameters Pθ, the numerator of the equation is the likelihood. In a Bayesian regression model, instead of obtaining point estimates of the model as did in the ordinary least square regression, the posterior distribution of the parameters was obtained given the data (D). In estimating the posterior distribution, closed-form solutions are only available to a limited number of prior distributions, such as the Gaussian (normal) distribution, see Equation (3). In situations where no closed-form solution available, the Markov chain Monte Carlo (MCMC) simulation can be used (Gelman et al., 2014). This study used an implementation of the MCMC called Hamiltonian Monte Carlo sampling or hybrid Monte Carlo sampling (Gelman et al., 2014). The stan language was used to create the Bayesian models (Carpenter et al., 2017).
Investigating long-term performance of flexible pavement using Bayesian multilevel models
Published in Road Materials and Pavement Design, 2023
Haimei Liang, Hongren Gong, Yiren Sun, Jiachen Shi, Lin Cong, Wenyang Han, Peng Guo
We used a type of Monte Carlo sampling algorithm, Hamiltonian Monte Carlo (HMC), to simulate the posterior distributions (Neal et al., 2011). We coded our Bayesian models using the Stan probabilistic programming language (Gelman et al., 2015). The concerned posterior distributions were simulated using five parallel Markov chains, with each containing 10,000 samples, in which 5000 samples were used for ‘warming up’ the chains. For details of training Bayesian models through HMC and Stan, please refer to McElreath (2020) and Chen et al. (2020). All parameters (including the intercept terms) were assigned a prior to a weakly informative normal distribution N(0,2.5), while the standard deviation term (σ) was assigned a non-negative distribution cauchy(0,1). Using weakly informative priors instead of diffusive (flat) prior distributions has been recommended by van de Schoot et al. (2021) and McElreath (2020).
Bayesian estimation of discrete choice models: a comparative analysis using effective sample size
Published in Transportation Letters, 2022
Jason Hawkins, Khandker Nurul Habib
We focus here on Stan for comparability with previous work. Stan has interfaces through R (RStan), Python (PyStan), Matlab (MatlabStan), among many other programming languages commonly used in the discrete choice and transportation modeling community. It has an active community of users and developers, as well as ample documentation. Error messages are highly informative, generally specifying the line number and specific details about the cause of the error. Importantly, the diagnostics provided with Stan substantially decrease model development time. Upon completion of inference, Stan outputs the potential scale reduction statistics and effective sample size for each parameter. It provides indicators to the analyst of model convergence and suggests modifications to obtain convergence. Tuning parameters for the algorithms are set at values found to be good starting values by the development team, often saving the analyst time by reducing the need to establish these values.
Hierarchical point process models for recurring safety critical events involving commercial truck drivers: A reliability framework for human performance modeling
Published in Journal of Quality Technology, 2022
Miao Cai, Amir Mehdizadeh, Qiong Hu, Mohammad Ali Alamdar Yazdi, Alexander Vinel, Karen C. Davis, Hong Xian, Fadel M. Megahed, Steven E. Rigdon
With a high-dimensional problem like the one we address here, MCMC will often require a very long time to draw samples from the posterior distribution (Betancourt 2018). While there are a number of engines to perform MCMC, we recommend using the statistical modeling and computing platform Stan to efficiently estimate the posterior distribution of parameters for PLP and JPLP. Stan leverages the power of Hamiltonian Monte Carlo and improves the efficiency of sampling from posterior distributions, which is very useful for estimating complex models. Stan also allows users to provide self-defined distributions and likelihood functions. We have hosted our Stan code and some sample data for estimating PLP and JPLP in the supplementary materials, so that the readers could apply the models to their own data.