Bayesian road safety analysis: Incorporation of past evidence and effect of hyper-prior choice

Miranda-Moreno, Luis F.; Heydari, Shahram; Lord, Dominique; Fu, Liping

doi:10.1016/j.jsr.2013.03.003

Cited by 24 publications

(19 citation statements)

References 39 publications

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“…They concluded that the two-stage Bayesian method was the best way to improve model fitting and provide the smallest credible intervals, for the reason that observed samples were treated as an extension of previous data. Miranda-Moreno et al (2013) simulated data from prior studies using different sample sizes and years of accident data, and combined this previous experience with current data. They found model parameter estimates can be significantly improved by using informative priors based on the findings from those prior studies.…”

Section: Statistical Modeling Methodsmentioning

confidence: 99%

Safety modeling of urban arterials in Shanghai, China

Wang

Fan

Chen

et al. 2015

Accident Analysis & Prevention

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Section: Statistical Modeling Methodsmentioning

confidence: 99%

Safety modeling of urban arterials in Shanghai, China

Wang

Fan

Chen

et al. 2015

Accident Analysis & Prevention

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“…The formulation of informative hyper priors for τ in Equations (8) and (9) has been used in Miranda-Moreno et al (2013) for the precision hyperparameter through a gamma distribution. However, the precision hyperparameter in their research comes from a hierarchical Poisson model for accident data, which is different from the Gaussian model (i.e., normal distribution model) used to estimate the treatment effect in RCTs.…”

Section: Hierarchical Bayes Modelmentioning

confidence: 99%

“…However, the precision hyperparameter in their research comes from a hierarchical Poisson model for accident data, which is different from the Gaussian model (i.e., normal distribution model) used to estimate the treatment effect in RCTs. In our study, in addition to developing hyper priors for the precision hyperparameter, which was the focus in previous studies of hierarchical Bayes models (Gelman, 2006b; Miranda-Moreno et al, 2013), we also formulated hyper priors for the mean hyperparameter based on the sampling distribution of effect size means, in an attempt to improve estimation accuracy for the treatment effect. The hyper priors in Equations (6) through (9) utilizing information from past studies are considered informative priors.…”

Section: Hierarchical Bayes Modelmentioning

confidence: 99%

“…However, the example provided in Gelman’s study did not explicitly indicate how the hyper priors were derived from the data. Outside educational research, hyper priors have received wider attention in road safety research (Farid et al, 2017; Heydari et al, 2014; Miranda-Moreno et al, 2013; B.-J. Park et al, 2010; Yu & Abdel-Aty, 2013).…”

Section: The Current Investigationmentioning

confidence: 99%

“…In spite of adding a second level in the model hierarchy, the specification of hyper priors is still crucial and can affect the modeling results to varying extents (Malinverno & Briggs, 2004; Miranda-Moreno et al, 2013). A few studies have investigated hierarchical models in various fields of research, including road safety analyses (Heydari et al, 2014; Lord & Miranda-Moreno, 2008; Miranda-Moreno et al, 2013; Yu & Abdel-Aty, 2013) and educational research (Gelman, 2006b; Jacobucci & Grimm, 2018). All demonstrated that the use of properly constructed informative hyper priors can enhance parameter estimates.…”

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confidence: 99%

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Hierarchical Bayes Approach to Estimate the Treatment Effect for Randomized Controlled Trials

Liang

Kamata

2020

Educational and Psychological Measurement

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One important issue in Bayesian estimation is the determination of an effective informative prior. In hierarchical Bayes models, the uncertainty of hyperparameters in a prior can be further modeled via their own priors, namely, hyper priors. This study introduces a framework to construct hyper priors for both the mean and the variance hyperparameters for estimating the treatment effect in a two-group randomized controlled trial. Assuming a random sample of treatment effect sizes is obtained from past studies, the hyper priors can be constructed based on the sampling distributions of the effect size mean and precision. The performance of the hierarchical Bayes approach was compared with the empirical Bayes approach (hyperparameters are fixed values or point estimates) and the ordinary least squares (OLS) method via simulation. The design factors for data generation included the sample treatment effect size, treatment/control group size ratio, and sample size. Each generated data set was analyzed using the hierarchical Bayes approach with three hyper priors, the empirical Bayes approach with twelve priors (including correct and inaccurate priors), and the OLS method. Results indicated that the proposed hierarchical Bayes approach generally outperformed the empirical Bayes approach and the OLS method, especially with small samples. When more sample effect sizes were available, the treatment effect was estimated more accurately regardless of the sample sizes. Practical implications and future research directions are discussed.

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