• Communications for Statistical Applications and Methods
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• v.29 no.5
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• pp.513-532
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• 2022

In this paper, the use of Bayes factors and the deviance information criterion for model selection are compared in a Bayesian accelerated life testing setup. In Bayesian accelerated life testing, the most used tool for model comparison is the deviance information criterion. An alternative and more formal approach is to use Bayes factors to compare models. However, Bayesian accelerated life testing models with more than one stressor often have mathematically intractable posterior distributions and Markov chain Monte Carlo methods are employed to obtain posterior samples to base inference on. The computation of the marginal likelihood is challenging when working with such complex models. In this paper, methods for approximating the marginal likelihood and the application thereof in the accelerated life testing paradigm are explored for dual-stress models. A simulation study is also included, where Bayes factors using the different approximation methods and the deviance information are compared.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1149-1160
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• 2011

Model selection and hypothesis testing problems in Bayesian inference are still debated between scholars. Bayesian factors traditionally used as a criterion in Bayesian hypothesis testing and model selection, are easy to understand but sometimes hard to compute. In addition, there are other model selection criterions such as DIC(Deviance Information Criterion) by Spiegelhalter et al. (2002) and Bayesian P-values for testing. In this paper, we briefly introduce the Bayesian hypothesis testing and model selection procedure. In addition we have applied a Bayesian inference to Swiss banknote data by a fitting logistic regression model and computing several test statistics to see if they provide consistent results.

• Communications for Statistical Applications and Methods
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• v.27 no.2
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• pp.189-199
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• 2020

This paper studies a Bayesian ordered multiple linear regression model with skew normal error. It is reasonable that the kind of inherent information available in an applied regression requires some constraints on the coefficients to be estimated. In addition, the assumption of normality of the errors is sometimes not appropriate in the real data. Therefore, to explain such situations more flexibly, we use the skew-normal distribution given by Sahu et al. (The Canadian Journal of Statistics, 31, 129-150, 2003) for error-terms including normal distribution. For Bayesian methodology, the Markov chain Monte Carlo method is employed to resolve complicated integration problems. Also, under the improper priors, the propriety of the associated posterior density is shown. Our Bayesian proposed model is applied to NZAPB's apple data. For model comparison between the skew normal error model and the normal error model, we use the Bayes factor and deviance information criterion given by Spiegelhalter et al. (Journal of the Royal Statistical Society Series B (Statistical Methodology), 64, 583-639, 2002). We also consider the problem of detecting an influential point concerning skewness using Bayes factors. Finally, concluding remarks are discussed.

• The Korean Journal of Applied Statistics
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• v.16 no.2
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• pp.365-376
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• 2003

In this paper we reviewed a variety of non-Gaussian time series models, and studied the model selection criteria such as AIC and BIC to select proper models. We also considered the likelihood ratio test and applied it to analysis of Polio data set.

• Safety and Health at Work
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• v.7 no.4
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• pp.322-325
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• 2016

Background: Musculoskeletal disorders (MSDs) are a common problem among carpet weavers. This study was undertaken to introduce affecting personal and occupational factors in developing the number of MSDs among carpet weavers. Methods: A cross-sectional study was performed among 862 weavers in seven towns with regard to workhouse location in urban or rural regions. Data were collected by using questionnaires that contain personal, workplace, and information tools and the modified Nordic MSDs questionnaire. Statistical analysis was performed by applying Poisson and negative binomial mixed models using a full Bayesian hierarchical approach. The deviance information criterion was used for comparison between models and model selection. Results: The majority of weavers (72%) were female and carpet weaving was the main job of 85.2% of workers. The negative binomial mixed model with lowest deviance information criterion was selected as the best model. The criteria showed the convergence of chains. Based on 95% Bayesian credible interval, the main job and weaving type variables statistically affected the number of MSDs, but variables age, sex, weaving comb, work experience, and carpet weaving looms were not significant. Conclusion: According to the results of this study, it can be concluded that occupational factors are associated with the number of MSDs developing among carpet weavers. Thus, using standard tools and decreasing hours of work per day can reduce frequency of MSDs among carpet weavers.

• Journal of the Korean Data and Information Science Society
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• v.25 no.1
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• pp.187-194
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• 2014

We consider a Bayesian nonignorable selection model to accommodate the selection bias. Markov chain Monte Carlo methods is known to be very useful to fit the nonignorable selection model. However, sensitivity to prior assumptions on parameters for selection mechanism is a potential problem. To quantify the sensitivity to prior assumption, the deviance information criterion and the conditional predictive ordinate are used to compare the goodness-of-fit under two different prior specifications. It turns out that the 'MLE' prior gives better fit than the 'uniform' prior in viewpoints of goodness-of-fit measures.

• Journal of the Korean Data and Information Science Society
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• v.27 no.5
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• pp.1225-1239
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• 2016

We investigate pediatric tumor incidence data collected by the Florida Association for Pediatric Tumor program using various models commonly used in disease mapping analysis. Particularly, we consider Poisson normal models with various conditional autoregressive structure for spatial dependence, a zero-in ated component to capture excess zero counts and a spatio-temporal model to capture spatial and temporal dependence, together. We found that intrinsic conditional autoregressive model provides the smallest Deviance Information Criterion (DIC) among the models when only spatial dependence is considered. On the other hand, adding an autoregressive structure over time decreases DIC over the model without time dependence component. We adopt weighted ranks squared error loss to identify high risk regions which provides similar results with other researchers who have worked on the same data set (e.g. Zhang et al., 2014; Wang and Rodriguez, 2014). Our results, thus, provide additional statistical support on those identied high risk regions discovered by the other researchers.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.65-83
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• 2022

Although various statistical methods have been developed to map time-dependent genetic factors, most identified genetic variants can explain only a small portion of the estimated genetic variation in longitudinal traits. Gene-gene and gene-time/environment interactions are known to be important putative sources of the missing heritability. However, mapping epistatic gene-gene interactions is extremely difficult due to the very large parameter spaces for models containing such interactions. In this paper, we develop a Gaussian process (GP) based nonparametric Bayesian variable selection method for longitudinal data. It maps multiple genetic markers without restricting to pairwise interactions. Rather than modeling each main and interaction term explicitly, the GP model measures the importance of each marker, regardless of whether it is mostly due to a main effect or some interaction effect(s), via an unspecified function. To improve the flexibility of the GP model, we propose a novel grid-based method for the within-subject dependence structure. The proposed method can accurately approximate complex covariance structures. The dimension of the covariance matrix depends only on the number of fixed grid points although each subject may have different numbers of measurements at different time points. The deviance information criterion (DIC) and the Bayesian predictive information criterion (BPIC) are proposed for selecting an optimal number of grid points. To efficiently draw posterior samples, we combine a hybrid Monte Carlo method with a partially collapsed Gibbs (PCG) sampler. We apply the proposed GP model to a mouse dataset on age-related body weight.

• Management Science and Financial Engineering
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• v.12 no.2
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• pp.19-35
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• 2006

We use the hierarchical Bayesian approach to describe the transition probabilities of a binary nonhomogeneous Markov chain. The Markov chain is used for describing the transition behavior of emotionally disturbed children in a treatment program. The effects of covariates on transition probabilities are assessed using a logit link function. To describe the time evolution of transition probabilities, we consider two modeling strategies. The first strategy is based on the concept of exchangeabiligy, whereas the second one is based on a first order Markov property. The deviance information criterion (DIC) measure is used to compare models with two different time dependent structures. The inferences are made using the Markov chain Monte Carlo technique. The developed methodology is applied to some real data.

• The Korean Journal of Applied Statistics
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• v.33 no.1
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• pp.47-59
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• 2020

In this paper, we present the longitudinal Markov binary regression model with t-link function when its transition order is known or unknown. It is assumed that logit or probit models are considered in binary regression models. Here, t-link function can be used for more flexibility instead of the probit model since the t distribution approaches to normal distribution as the degree of freedom goes to infinity. A Markov regression model is considered because of the longitudinal data of each individual data set. We propose Bayesian method to determine the transition order of Markov regression model. In particular, we use the deviance information criterion (DIC) (Spiegelhalter et al., 2002) of possible models in order to determine the transition order of the Markov binary regression model if the transition order is known; however, we compute and compare their posterior probabilities if unknown. In order to overcome the complicated Bayesian computation, our proposed model is reconstructed by the ideas of Albert and Chib (1993), Kuo and Mallick (1998), and Erkanli et al. (2001). Our proposed method is applied to the simulated data and real data examined by Sommer et al. (1984). Markov chain Monte Carlo methods to determine the optimal model are used assuming that the transition order of the Markov regression model are known or unknown. Gelman and Rubin's method (1992) is also employed to check the convergence of the Metropolis Hastings algorithm.