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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 severity is modeled as absolute numbers of oil spilled (tons) per accident. The expected oil spill in each area is modeled using a Lognormal (LOGNO) distribution (e.g. Burgherr et al., 2015). In this case, at a first approximation, the spill is considered independent from the area; therefore, no spatial random effects are included. The LOGNO distribution is commonly described by two parameters, namely the scale σi and location μi, which are used to define the mean value and variance of the distribution (e.g. Spada et al., 2014). In this study, the LOGNO distribution employed for the Bayesian Hierarchical modeling is described by mean and precision parameters, where the latter is the inverse of the variance. Hierarchical models are defined for the mean and standard deviation of the posterior and are modeled using a normal and gamma distributions, respectively. All the hyperparameters of both the mean and standard deviation are thus modeled with non-informative distributions.
Robust Bayesian hierarchical modeling and inference using scale mixtures of normal distributions
Published in IISE Transactions, 2022
Linhan Ouyang, Shichao Zhu, Keying Ye, Chanseok Park, Min Wang
Quality prediction is an essential task in manufacturing processes, as its accuracy has a significant impact on quality improvement and control. The SUR model has proved to be an effective modeling technique when quality features are highly correlated. As noted above, non-normality and high correlations are common phenomena in the LCR processes. This article aims to develop a RBSUR model that deals with these issues. Specifically, we first incorporated the class of scale mixtures of multivariate normal distributions for the construction of the likelihood function. We then constructed a Bayesian hierarchical modeling framework and developed an MCMC sampling algorithm to generate posterior samples from the joint posterior distribution to obtain the robust Bayesian estimates. An LCR process and simulation studies are adopted to illustrate the superior performance of the proposed Bayesian procedures. Numerical results showed that the RBSUR model achieves better performance than the classic SUR models with the multivariate normal errors.