• Proceedings of the Korean Information Science Society Conference
• /
• 2007.06c
• /
• pp.263-266
• /
• 2007

This paper discusses the Bayesian statistical inference. This paper discusses the Bayesian inference, MCMC (Markov Chain Monte Carlo) integration, MCMC method, Metropolis-Hastings algorithm, Gibbs sampling, Maximum likelihood estimation, Expectation Maximization algorithm, missing data processing, and BMA (Bayesian Model Averaging). The Bayesian statistical inference is used to process a large amount of data in the areas of biology, medicine, bioengineering, science and engineering, and general data analysis and processing, and provides the important method to draw the optimal inference result. Lastly, this paper discusses the method of principal component analysis. The PCA method is also used for data analysis and inference.

• Journal of the Korean Statistical Society
• /
• v.20 no.1
• /
• pp.44-56
• /
• 1991

For all pairwise comparisons of treatments, Bayesian simultaneous confidence intervals are proposed and studied. First Bayesian solutions are obtained for a fixed prior, and then prior parameters are estimated by a parametric empirical Bayesian method. The nominal confidence level is shown to be controlled asymptotically. An extension to the unbalanced design is also considered.

• Journal of the Korean Statistical Society
• /
• v.34 no.3
• /
• pp.245-261
• /
• 2005

The marginal distribution of X is considered when (X, Y) has a truncated bivariate t-distribution. This paper mainly focuses on the marginal nontruncated distribution of X where Y is truncated below at its mean and its observations are not available. Several properties and applications of this distribution, including relationship with Azzalini's skew-normal distribution, are obtained. To circumvent inferential problem arises from adopting the frequentist's approach, a Bayesian method utilizing a data augmentation method is suggested. Illustrative examples demonstrate the performance of the method.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.17 no.5
• /
• pp.645-652
• /
• 2016

The statistical modeling of input random variables is necessary in reliability analysis, reliability-based design optimization, and statistical validation and calibration of analysis models of mechanical systems. In statistical modeling methods, there are the Akaike Information Criterion (AIC), AIC correction (AICc), Bayesian Information Criterion, Maximum Likelihood Estimation (MLE), and Bayesian method. Those methods basically select the best fitted distribution among candidate models by calculating their likelihood function values from a given data set. The number of data or parameters in some methods are considered to identify the distribution types. On the other hand, the engineers in a real field have difficulties in selecting the statistical modeling method to obtain a statistical model of the experimental data because of a lack of knowledge of those methods. In this study, commonly used statistical modeling methods were compared using statistical simulation tests. Their advantages and disadvantages were then analyzed. In the simulation tests, various types of distribution were assumed as populations and the samples were generated randomly from them with different sample sizes. Real engineering data were used to verify each statistical modeling method.

• Journal for History of Mathematics
• /
• v.11 no.1
• /
• pp.68-77
• /
• 1998

There are two approach methods widely in statistical inferences. First is sampling theory methods and the other is Bayesian methods. In this paper, we will introduce the most basic differences of the two approach methods. Especially, we investigate and introduce the historical origin of Bayesian methods in Statistical inferences which is currently used. Also, we introduce the some characteristics of sampling theory method and Bayesian methods.

• Communications for Statistical Applications and Methods
• /
• v.13 no.3
• /
• pp.701-718
• /
• 2006

In cancer microarray experiments, the experimenter or patient which is nested in each experimenter often shows quite heterogeneous error variability, which should be estimated for identifying a source of variation. Our study describes a Bayesian method which utilizes clinical information for identifying a set of DE genes for the class of subtypes as well as assesses and examines the experimenter effect and patient effect which is nested in each experimenter as a source of variation. We propose a Bayesian multilevel mixed effect model based on analysis of covariance (ANACOVA). The Bayesian multilevel mixed effect model is a combination of the multilevel mixed effect model and the Bayesian hierarchical model, which provides a flexible way of defining a suitable correlation structure among genes.

• Communications for Statistical Applications and Methods
• /
• v.24 no.1
• /
• pp.67-80
• /
• 2017

Over the last few decades, ensemble forecasts based on global climate models have become an important part of climate forecast due to the ability to reduce uncertainty in prediction. Moreover in ensemble forecast, assessing the prediction uncertainty is as important as estimating the optimal weights, and this is achieved through a probabilistic forecast which is based on the predictive distribution of future climate. The Bayesian model averaging has received much attention as a tool of probabilistic forecasting due to its simplicity and superior prediction. In this paper, we propose a new Bayesian model averaging method for probabilistic ensemble forecasting. The proposed method combines a deterministic ensemble forecast based on a multivariate regression approach with Bayesian model averaging. We demonstrate that the proposed method is better in prediction than the standard Bayesian model averaging approach by analyzing monthly average precipitations and temperatures for ten cities in Korea.

• Proceedings of the KSRS Conference
• /
• 2002.10a
• /
• pp.394-399
• /
• 2002

In this paper, Multisource data classification methods based on Bayesian formula are considered. For this decision fusion scheme, the individual data sources are handled separately by statistical classification algorithms and then Bayesian fusion method is applied to integrate from the available data sources. This method includes the combination of each expert decisions where the weights of the individual experts represent the reliability of the sources. The reliability measure used in the statistical approach is common to all pixels in previous work. In this experiment, the weight factors have been assigned to have different value for all pixels in order to improve the integrated classification accuracies. Although most implementations of Bayesian classification approaches assume fixed a priori probabilities, we have used adaptive a priori probabilities by iteratively calculating the local a priori probabilities so as to maximize the posteriori probabilities. The effectiveness of the proposed method is at first demonstrated on simulations with artificial and evaluated in terms of real-world data sets. As a result, we have shown that Bayesian statistical fusion scheme performs well on multispectral data classification.

• Communications for Statistical Applications and Methods
• /
• v.29 no.3
• /
• pp.287-299
• /
• 2022

In radiation epidemiology, the excess relative risk (ERR) model is used to determine the dose-response relationship. In general, the dose-response relationship for the ERR model is assumed to be linear, linear-quadratic, linear-threshold, quadratic, and so on. However, since none of these functions dominate other functions for expressing the dose-response relationship, a Bayesian semiparametric method using splines has recently been proposed. Thus, we improve the Bayesian semiparametric method for the selection of the tuning parameters for splines as the number and location of knots using a Bayesian knot selection method. Equally spaced knots cannot capture the characteristic of radiation exposed dose distribution which is highly skewed in general. Therefore, we propose a nonparametric Bayesian knot selection method based on a Dirichlet process mixture model. Inference of the spline coefficients after obtaining the number and location of knots is performed in the Bayesian framework. We apply this approach to the life span study cohort data from the radiation effects research foundation in Japan, and the results illustrate that the proposed method provides competitive curve estimates for the dose-response curve and relatively stable credible intervals for the curve.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.15 no.5
• /
• pp.2603-2609
• /
• 2014

Reliability analysis of mechanical systems requires statistical modeling of input random variables such as distribution function types and statistical parameters that affect the performance of the mechanical systems. Some random variables are correlated, but considered as independent variables or wrong assumptions on input random variables have been used. In this paper, joint distributions were modeled using copulas and Bayesian method from limited number of data. To verify the proposed method, statistical simulation tests were carried out for various number of samples and correlation coefficients. As a result, the Bayesian method selected the most probable copula types among candidate copulas even though the candidate copula shapes are similar for low correlations or the number of data is limited. The most probable copulas also yielded similar reliabilities with the true reliability obtained from a true copula, so that it can be concluded that the Bayesian method provides accurate statistical modeling for the reliability analysis.