• Journal of Korean Society for Quality Management
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• v.37 no.4
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• pp.16-22
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• 2009

The inflection S-shaped software reliability growth model (SRGM) proposed by Ohba(1984) is one of the most commonly used models and has been discussed by many authors. The main purpose of this paper is to estimate the parameters of Ohba's SRGM within the Bayesian framework by applying the Markov chain Monte Carlo techniques. While the maximum likelihood estimates for these parameters are well known, the Bayesian method for the inflection S-shaped SRGM have not been discussed in the literature. The proposed methods can be quite flexible depending on the choice of prior distributions for the parameters of interests. We also compare the Bayesian methods with the maximum likelihood method numerically based on the real data.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.8 no.11
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• pp.27-34
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• 1985

Recently the distributed lag models for time series data have been used in several quantitative analyses. But the analyses of time series which have the serial correlations in error terms and the lagged values of dependent variables violate the hypothesis of OLS method. This paper suggests that the approach technique of distributed lay model with serial correlation should be applied by the Bayesian inference to estimate the parameters. For the application of distributed lag model by Bayesian analysis, the data for monthly consumption expenditure per household by items of commodities from 1972 to 1981 are used in order to estimate the lagged coefficient of processed food and the regression coefficient of the food and beverage.

• The Korean Journal of Applied Statistics
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• v.17 no.2
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• pp.281-301
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• 2004

In this paper we consider the change point problem in a sequence of univariate normal observations. We want to know whether there is any change point or not. In case a change point exists, we will identify its change type. Namely, it can be a mean change, a variance change, or both the mean and variance change. The intrinsic Bayes factors of Berger and Pericchi (1996, 1998) are used to find the type of optimal change model. The Gibbs sampling including the Metropolis-Hastings algorithm is used to estimate all the parameters in the change model. These methods are checked via simulation and applied to the winter average temperature data in Seoul.

• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.182-182
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• 2015

우리나라에서는 강우관측시스템의 지역적 불균형으로 상대적으로 소규모 저수지의 경우 미계측유역의 특성을 가지며, 신뢰성 있는 강우량, 유출량, 증발량 자료가 매우 부족한 실정이다. 다목적댐 유역과 같은 계측유역의 경우 상류유역의 유입량 자료의 확보가 용이하지만 대부분의 유역의 경우 계측장비가 부족하여 신뢰성이 확보된 유입량 자료를 얻는데 많은 어려움이 있다. 본 연구에서는 미계측유역의 유입량 산정을 위하여 계측유역을 대상으로 강우-유출 모형의 매개변수를 산정하였으며, 산정된 매개변수를 유역특성인자와의 상관성을 토대로 다중선형회귀분석기법(multiple linear regression, MLR)을 적용하여 지역화(regionalization)를 위한 회귀식을 도출하였다. 이를 위해 양질의 유량자료가 확보된 K-water 17개 댐 유역을 대상으로 매개변수를 산정하였으며 이 중 2개의 댐 유역을 미계측유역으로 간주하여 개발된 모형을 검증하였다. 대부분의 통계 지표에서 우수한 모의능력을 확인하였으며, 본 연구를 통하여 개발된 지역화 기법을 미계측유역에 활용한다면 보다 정량적이고 효율적인 수자원 계획이 가능할 것으로 판단된다. 향후 연구로는 불확실성을 고려한 Bayesian GLM 모형을 이용한 지역화기법을 개발하여 매개변수의 불확실성까지 고려할 수 있는 방안을 모색하고자 한다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.4B
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• pp.389-397
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• 2010

This study introduced a Bayesian based frequency analysis in which the statistical trend analysis for hydrologic extreme series is incorporated. The proposed model employed Gumbel extreme distribution to characterize extreme events and a fully coupled bayesian frequency model was finally utilized to estimate design rainfalls in Seoul. Posterior distributions of the model parameters in both Gumbel distribution and trend analysis were updated through Markov Chain Monte Carlo Simulation mainly utilizing Gibbs sampler. This study proposed a way to make use of nonstationary frequency model for dynamic risk analysis, and showed an increase of hydrologic risk with time varying probability density functions. The proposed study showed advantage in assessing statistical significance of parameters associated with trend analysis through statistical inference utilizing derived posterior distributions.

• Journal of Korea Water Resources Association
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• v.41 no.3
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• pp.325-340
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• 2008

This study employs Bayesian multiple regression analysis using the ordinary least squares method for regional low flow frequency analysis. The parameter estimates using the Bayesian multiple regression analysis were compared to conventional analysis using the t-distribution. In these comparisons, the mean values from the t-distribution and the Bayesian analysis at each return period are not significantly different. However, the difference between upper and lower limits is remarkably reduced using the Bayesian multiple regression. Therefore, from the point of view of uncertainty analysis, Bayesian multiple regression analysis is more attractive than the conventional method based on a t-distribution because the low flow sample size at the site of interest is typically insufficient to perform low flow frequency analysis. Also, we performed low flow prediction, including confidence interval, at two ungauged catchments in the Nakdong River basin using the developed Bayesian multiple regression model. The Bayesian prediction proves effective to infer the low flow characteristic at the ungauged catchment.

• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.833-845
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• 2011

This paper conducts a statistical analysis of extreme values for both daily log-returns and daily negative log-returns, which are computed using a collection of KOSPI data from January 3, 1998 to August 31, 2011. The Poisson-GPD model is used as a statistical analysis model for extreme values and the maximum likelihood method is applied for the estimation of parameters and extreme quantiles. To the Poisson-GPD model is also added the Bayesian method that assumes the usual noninformative prior distribution for the parameters, where the Markov chain Monte Carlo method is applied for the estimation of parameters and extreme quantiles. According to this analysis, both the maximum likelihood method and the Bayesian method form the same conclusion that the distribution of the log-returns has a shorter right tail than the normal distribution, but that the distribution of the negative log-returns has a heavier right tail than the normal distribution. An advantage of using the Bayesian method in extreme value analysis is that there is nothing to worry about the classical asymptotic properties of the maximum likelihood estimators even when the regularity conditions are not satisfied, and that in prediction it is effective to reflect the uncertainties from both the parameters and a future observation.

• Journal of Korea Water Resources Association
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• v.50 no.2
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• pp.75-87
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• 2017

In recent decades, extreme events have been significantly increased over the Korean Peninsula due to climate variability and climate change. The potential changes in hydrologic cycle associated with the extreme events increase uncertainty in water resources planning and designing. For these reasons, a reliable changing point analysis is generally required to better understand regime changes in hydrologic time series at watershed scale. In this study, a hierarchical changing point analysis approach that can apply in a watershed scale is developed by combining the existing changing point analysis method and hierarchical Bayesian method. The proposed model was applied to the selected stations that have annual rainfall data longer than 40 years. The results showed that the proposed model can quantitatively detect the shift in precipitation in the middle of 1990s and identify the increase in annual precipitation compared to the several decades prior to the 1990s. Finally, we explored the changes in precipitation and sea level pressure in the context of large-scale climate anomalies using reanalysis data, for a given change point. It was concluded that the identified large-scale patterns were substantially different from each other.

• Journal of the Korean Data and Information Science Society
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• v.26 no.4
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• pp.813-826
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• 2015

This research deals with an estimation method for kinetic reaction model. The kinetic reaction model is a model to explain spread or changing process based on interaction between species on the Biochemical area. This model can be applied to a model for disease spreading as well as a model for system Biology. In the search, we assumed that the spread of species is stochastic and we construct the reaction model based on stochastic movement. We utilized Gillespie algorithm in order to construct likelihood function. We introduced a Bayesian estimation method using Markov chain Monte Carlo methods that produces more stable results. We applied the Bayesian estimation method to the Lotka-Volterra model and gene transcription model and had more stable estimation results.

• The Korean Journal of Applied Statistics
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• v.33 no.2
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• pp.123-136
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• 2020

It is common to encounter correlated multiple outcomes measured on the same subject in various research fields. In developmental toxicity studies, presence of malformed pups and fetal weight are measured on the pregnant dams exposed to different levels of a toxic substance. Joint analysis of such two outcomes can result in more efficient inferences than separate models for each outcome. Most methods for joint modeling assume a normal distribution as random effects. However, in developmental toxicity studies, the response distributions may change irregularly in location and shape as the level of toxic substance changes, which may not be captured by a normal random effects model. Motivated by applications in developmental toxicity studies, we propose a Bayesian joint model for binary and continuous outcomes. In our model, we incorporate a skewed logit model for the binary outcome to allow the response distributions to have flexibly in both symmetric and asymmetric shapes on the toxic levels. We apply our proposed method to data from a developmental toxicity study of diethylhexyl phthalate.