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Determinants of health complaints of Bodetabek commuter workers using Bayesian multilevel logistic regression
Published in Yuli Rahmawati, Peter Charles Taylor, Empowering Science and Mathematics for Global Competitiveness, 2019
When the posterior distribution was difficult to derive mathematically, it was approximated using Markov Chain Monte Carlo (MCMC) (Hox, 2010). MCMC is a simulation technique that can generate random samples from a complex posterior distribution. Through a large number of simulated random samples, it will be possible to calculate the posterior mean, standard deviation, density plot, and quintiles of this distribution (Browne, 2017). In the Bayesian MCMC approach, to test the model fit (goodness of fit), we can compare the Deviance Information Criterion (DIC) from each model. () DIC=D¯+pD
Toward the integration of uncertainty and probabilities in spatial multi-criteria risk analysis
Published in Stein Haugen, Anne Barros, Coen van Gulijk, Trond Kongsvik, Jan Erik Vinnem, Safety and Reliability – Safe Societies in a Changing World, 2018
The MCMC algorithm is run for 30,000 iterations, following a burn-in of 3,000 updates, which is also used to train the model, for both frequency and severity cases. According to the Gelman-Rubin diagnostic (e.g. Gelman and Rubin, 1992), the simulated chains converged adequately in the MCMC practice implemented in this study for both cases. Furthermore, the models for both frequency and severity distributions have been validated using the Deviance Information Criterion (DIC), which tests how good the proposed model predicts a replicate dataset which has the same structure as the observed one, e.g. the historical observations (e.g. Gelman, 2003).
Bayesian Statistical Methods
Published in Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos, Statistical and Econometric Methods for Transportation Data Analysis, 2020
Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos
To encourage model parsimony—capturing complexity as simply as possible—a penalized measure (akin to the adjusted R-square measure in linear regression) is obtained by applying Akaike’s information criterion (Akaike, 1973) to obtain the deviance information criterion (Spiegelhalter et al., 2002), expressed as () DIC=D+2porDIC=D′+2p
Bayesian probability of agreement for comparing survival or reliability functions with parametric lifetime regression models
Published in Quality Engineering, 2020
Nathaniel T. Stevens, Lu Lu, Christine M. Anderson-Cook, Steven E. Rigdon
We conclude this section by considering alternative distributional assumptions for the time to first exacerbation. Figure 12 shows the estimated survival curves as a function of time for both the placebo and rhDNase groups by using the lognormal (left) and gamma (right) models. We can see both models provide similar estimates to the Weibull model for the treatment group. However, the different models yield slightly different survival estimates for the placebo group: the Weibull model consistently provides higher survival probability estimates, while the gamma model provides the lowest. Figure 13 shows the estimated BPA contours (with ) for the two alternative models. As expected, the BPA values based on fitting the gamma regression model are slightly lower than the lognormal model when t and FEV are both small. However, the difference between models is small, which suggests that all three models fit the observed data reasonably consistently. If desired, the deviance information criterion (DIC) (Spiegelhalter et al. 2002) can be used for formal model selection and comparison. However, the robustness of the BPA results to the choice of distribution is reassuring; whether one uses the Weibull, lognormal, or gamma models has little effect on our conclusions about the comparability of the survival experience in the placebo versus the rhDNase group.
Traffic safety analysis and model updating for freeways using Bayesian method
Published in Journal of Transportation Safety & Security, 2023
Xuesong Wang, Qi Zhang, Xiaohan Yang, Yingying Pei, Jinghui Yuan
The deviance information criterion (DIC) is a Bayesian measure of model fitting and complexity. A smaller DIC is preferred, and it can be defined is as follows: where denotes the Bayesian deviance of the estimated parameter, and is the posterior mean of Because is a measure of model fitting, can be viewed as the effective number of parameters, which indicates the complexity of the model.
Macro-level hazardous material transportation safety analysis in China using a Bayesian negative binomial model combined with conditional autoregression prior
Published in Journal of Transportation Safety & Security, 2022
Shiwen Zhang, Shengdi Chen, Yingying Xing, H. Michael Zhang, Jian Lu, Sijin Long
The deviance information criterion (DIC) is a measure of model comparison and adequacy (Spiegelhalter et al. 2002). The smaller the value of DIC is, the better the model will be (Equation (9)). where is the posterior mean of the parameters involved in model m. D (θm, m) is the usual deviance measure, is its posterior mean, and is interpreted as the number of “effective” parameters. The smaller DIC values indicate a better-fitting model.