• 품질경영학회지
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• 제27권3호
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• pp.125-141
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• 1999

Bayesian inference and model selection method for software reliability growth models are studied. Software reliability growth models are used in testing stages of software development to model the error content and time intervals between software failures. In this paper, we could avoid the multiple integration by the use of Gibbs sampling, which is a kind of Markov Chain Monte Carlo method to compute the posterior distribution. Bayesian inference and model selection method for Jelinski-Moranda and Goel-Okumoto and Schick-Wolverton models in software reliability with Poisson prior information are studied. For model selection, we explored the relative error.

• Communications for Statistical Applications and Methods
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• 제13권3호
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• pp.685-699
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• 2006

Commercial banks and other related areas have developed internal models to better quantify their financial risks. Since an appropriate credit risk model plays a very important role in the risk management at financial institutions, it needs more accurate model which forecasts the credit losses, and statistical inference on that model is required. In this paper, we propose a new method for estimating a default rate. It is a Bayesian approach using the power prior which allows for incorporating of historical data to estimate the default rate. Inference on current data could be more reliable if there exist similar data based on previous studies. Ibrahim and Chen (2000) utilize these data to characterize the power prior. It allows for incorporating of historical data to estimate the parameters in the models. We demonstrate our methodologies with a real data set regarding SOHO data and also perform a simulation study.

• Nuclear Engineering and Technology
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• 제56권7호
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• pp.2704-2710
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• 2024

Nuclear archaeology research provides scientific methods to reconstruct the operating histories of fissile material production facilities to account for past fissile material production. While it has typically focused on analyzing material in permanent reactor structures, spent fuel or high-level waste also hold information about the reactor operation. In this computational study, we explore a Bayesian inference framework for reconstructing the operational history from measurements of isotope ratios from a sample of nuclear waste. We investigate two different inference models. The first model discriminates between three potential reactors of origin (Magnox, PWR, and PHWR) while simultaneously reconstructing the fuel burnup, time since irradiation, initial enrichment, and average power density. The second model reconstructs the fuel burnup and time since irradiation of two batches of waste in a mixed sample. Each of the models is applied to a set of simulated test data, and the performance is evaluated by comparing the highest posterior density regions to the corresponding parameter values of the test dataset. Both models perform well on the simulated test cases, which highlights the potential of the Bayesian inference framework and opens up avenues for further investigation.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2008년도 추계학술대회A
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• pp.1331-1336
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• 2008

This paper suggests a method using Bayesian inference to estimate the parameters of Weibull distribution and acceleration parameters under the condition that the stresses are time-dependent functions. A Bayesian model based on the discrete time approximation is formulated to infer the parameters of interest from the failure data of the virtual tests and a statistical analysis is considered to decide the most probable mean values of the parameters for reasoning of the failure data.

• Communications for Statistical Applications and Methods
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• 제29권2호
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• pp.239-250
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• 2022

In many applications, we frequently encounter correlated multiple outcomes measured on the same subject. Joint modeling of such multiple outcomes can improve efficiency of inference compared to independent modeling. For instance, in developmental toxicity studies, fetal weight and number of malformed pups are measured on the pregnant dams exposed to different levels of a toxic substance, in which the association between such outcomes should be taken into account in the model. The number of malformations may possibly have many zeros, which should be analyzed via zero-inflated count models. Motivated by applications in developmental toxicity studies, we propose a Bayesian joint modeling framework for continuous and count outcomes with excess zeros. In our model, zero-inflated Poisson (ZIP) regression model would be used to describe count data, and a subject-specific random effects would account for the correlation across the two outcomes. We implement a Bayesian approach using MCMC procedure with data augmentation method and adaptive rejection sampling. We apply our proposed model to dose-response analysis in a developmental toxicity study to estimate the benchmark dose in a risk assessment.

• Asian Pacific Journal of Cancer Prevention
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• 제15권14호
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• pp.5571-5575
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• 2014

Background: The ability to predict the survival time of breast cancer patients is important because of the potential high morbidity and mortality associated with the disease. To develop a predictive inference for determining the survival of breast cancer patients, we applied a novel Bayesian method. In this paper, we propose the development of a databased statistical probability model and application of the Bayesian method to predict future survival times for White Hispanic female breast cancer patients, diagnosed in the US during 1973-2009. Materials and Methods: A stratified random sample of White Hispanic female patient survival data was selected from the Surveillance Epidemiology and End Results (SEER) database to derive statistical probability models. Four were considered to identify the best-fit model. We used three standard model-building criteria, which included Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), and Deviance Information Criteria (DIC) to measure the goodness of fit. Furthermore, the Bayesian method was used to derive future survival inferences for survival times. Results: The highest number of White Hispanic female breast cancer patients in this sample was from New Mexico and the lowest from Hawaii. The mean (SD) age at diagnosis (years) was 58.2 (14.2). The mean (SD) of survival time (months) for White Hispanic females was 72.7 (32.2). We found that the exponentiated Weibull model best fit the survival times compared to other widely known statistical probability models. The predictive inference for future survival times is presented using the Bayesian method. Conclusions: The findings are significant for treatment planning and health-care cost allocation. They should also contribute to further research on breast cancer survival issues.

• Journal of the Korean Data and Information Science Society
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• 제14권1호
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• pp.1-9
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• 2003

In this paper we discuss Bayesian computation and model selection for Littlewood-Verrall model using Gibbs sampling. A numerical example with a simulated data is given.

• 한국정보처리학회논문지
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• 제7권3호
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• pp.852-861
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• 2000

Software reliability growth models are used in testing stages of software development to model the error content and time intervals betwewn software failures. In this paper, using priors for the number of fault with the negative binomial distribution nd the error rate with gamma distribution, Bayesian inference and model selection method for Jelinski-Moranda and Goel-Okumoto and Schick-Wolverton models in software reliability. For model selection, we explored the sum of the relative error, Braun statistic and median variation. In Bayesian computation process, we could avoid the multiple integration by the use of Gibbs sampling, which is a kind of Markov Chain Monte Carolo method to compute the posterior distribution. Using simulated data, Bayesian inference and model selection is studied.

• Structural Engineering and Mechanics
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• 제63권1호
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• pp.47-53
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• 2017

The fundamental goal of this study is to minimize the uncertainty of the median fragility curve and to assess the structural vulnerability under earthquake excitation. Bayesian Inference with Markov Chain Monte Carlo (MCMC) simulation has been presented for efficient collapse response assessment of the independent intake water tower. The intake tower is significantly used as a diversion type of the hydropower station for maintaining power plant, reservoir and spillway tunnel. Therefore, the seismic fragility assessment of the intake tower is a pivotal component for estimating total system risk of the reservoir. In this investigation, an asymmetrical independent slender reinforced concrete structure is considered. The Bayesian Inference method provides the flexibility to integrate the prior information of collapse response data with the numerical analysis results. The preliminary information of risk data can be obtained from various sources like experiments, existing studies, and simplified linear dynamic analysis or nonlinear static analysis. The conventional lognormal model is used for plotting the fragility curve using the data from time history simulation and nonlinear static pushover analysis respectively. The Bayesian Inference approach is applied for integrating the data from both analyses with the help of MCMC simulation. The method achieves meaningful improvement of uncertainty associated with the fragility curve, and provides significant statistical and computational efficiency.

• Nuclear Engineering and Technology
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• 제53권1호
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• pp.304-313
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• 2021

Nickel base Alloy X-750, which is used as fastener parts in light-water reactor (LWR), has experienced many failures by environmentally assisted cracking (EAC). In order to improve the reliability of passive components for nuclear power plants (NPP's), it is necessary to study the failure mechanism and to predict crack growth behavior by developing a probabilistic failure model. In this study, The Bayesian inference was employed to reduce the uncertainties contained in EAC modeling parameters that have been established from experiments with Alloy X-750. Corrosion fatigue crack growth rate model (FCGR) was developed by fitting into Paris' Law of measured data from the several fatigue tests conducted either in constant load or constant ΔK mode. These parameters characterizing the corrosion fatigue crack growth behavior of X-750 were successfully updated to reduce the uncertainty in the model by using the Bayesian inference method. It is demonstrated that probabilistic failure models for passive components can be developed by updating a laboratory model with field-inspection data, when crack growth rates (CGRs) are low and multiple inspections can be made prior to the component failure.