• Journal of the Korean Data and Information Science Society
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• 제27권6호
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• pp.1645-1651
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• 2016

A lot of data, particularly in the medical field, contain variables that have a measurement error such as blood pressure and body mass index. On the other hand, recently smoothing methods are often used to solve a complex scientific problem. In this paper, we study a Bayesian curve-fitting under functional measurement error model. Especially, we extend our previous model by incorporating covariates free of measurement error. In this paper, we consider penalized splines for non-linear pattern. We employ a hierarchical Bayesian framework based on Markov Chain Monte Carlo methodology for fitting the model and estimating parameters. For application we use the data from the fifth wave (2012) of the Korea National Health and Nutrition Examination Survey data, a national population-based data. To examine the convergence of MCMC sampling, potential scale reduction factors are used and we also confirm a model selection criteria to check the performance.

• Journal of the Korean Statistical Society
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• 제31권2호
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• pp.177-198
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• 2002

The estimation of variance components or variance ratios in linear model is an important issue in plant or animal breeding fields, and various estimation methods have been devised to estimate variance components or variance ratios. However, many traits of economic importance in those fields are observed as dichotomous or polychotomous outcomes. The usual estimation methods might not be appropriate for these cases. Recently threshold linear model is considered as an important tool to analyze discrete traits specially in animal breeding field. In this note, we consider a hierarchical Bayesian method for the threshold animal model. Gibbs sampler for making full Bayesian inferences about random effects as well as fixed effects is described to analyze jointly discrete traits and continuous traits. Numerical example of the model with two discrete ordered categorical traits, calving ease of calves from born by heifer and calving ease of calf from born by cow, and one normally distributed trait, birth weight, is provided.

• Journal of the Korean Data and Information Science Society
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• 제26권3호
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• pp.749-754
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• 2015

This article presents Bayesian approach to regression splines with knots on a grid of equally spaced sample quantiles of the independent variables under functional measurement error model.We consider small area model by using penalized splines of non-linear pattern. Specifically, in a basis functions of the regression spline, we use radial basis functions. To fit the model and estimate parameters we suggest a hierarchical Bayesian framework using Markov Chain Monte Carlo methodology. Furthermore, we illustrate the method in an application data. We check the convergence by a potential scale reduction factor and we use the posterior predictive p-value and the mean logarithmic conditional predictive ordinate to compar models.

• Journal of the Korean Data and Information Science Society
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• 제26권3호
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• pp.755-762
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• 2015

One of the main objectives of the U.S. Census Bureau is the proper estimation of median household income for small areas. These estimates have an important role in the formulation of various governmental decisions and policies. Since direct survey estimates are available annually for each state or county, it is desirable to exploit the longitudinal trend in income observations in the estimation procedure. In this study, we consider Fay-Herriot type small area models which include time-specific random effect to accommodate any unspecified time varying income pattern. Analysis is carried out in a hierarchical Bayesian framework using Markov chain Monte Carlo methodology. We have evaluated our estimates by comparing those with the corresponding census estimates of 1999 using some commonly used comparison measures. It turns out that among three types of time-specific random effects the small area model with a time series random walk component provides estimates which are superior to both direct estimates and the Census Bureau estimates.

• Management Science and Financial Engineering
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• 제12권2호
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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.

• Journal of the Korean Statistical Society
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• 제29권2호
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• pp.155-168
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• 2000

Regarding to multiple comparison problem (MCP) of k normal population variances, we suggest a Bayesian method for calculating posterior probabilities for various hypotheses of equality among population variances. This leads to a simple method for obtaining pairwise comparisons of variances in a statistical experiment with a partition on the parameter space induced by equality and inequality relationships among the variances. The method is derived from the fact that certain features of the hierarchical nonparametric family of Dirichlet process priors, in general, make it amenable to solving the MCP and estimating the posterior probabilities by means of posterior simulation, the Gibbs sampling. Two examples are illustrated for the method. For these examples, the method is straightforward for specifying distributionally and to implement computationally, with output readily adapted for required comparison.

• 응용통계연구
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• 제27권2호
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• pp.263-275
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• 2014

본 연구에서는 비동차 마코프 체인에서 개체들의 전이 행태를 분석하기 위한 계층적 베이지안 방법론을 사용하여 혼합 효과 모델을 소개 하였다. 모델의 모수들에 대한 사후분포가 분석적으로 구해질 수 없는 형태를 가지기 때문에 깁스(Gibbs) 샘플링 시뮬레이션 방법을 사용하여 조건부 사후확률로부터 샘플이 추출되었고, 실제 자료분석을 예를 사용하였다.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2005년도 한국컴퓨터종합학술대회 논문집 Vol.32 No.1 (B)
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• pp.724-726
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• 2005

베이지안망(Bayesian network)은 다수의 변수들 사이의 확률적 관계(조건부독립성: conditional independence)를 그래프 구조로 표현하는 모델이다. 이러한 베이지안망은 비감독학습(unsupervised teaming)을 통한 데이터마이닝에 적합하다. 이를 위해 데이터로부터 베이지안망의 구조와 파라미터를 학습하게 된다. 주어진 데이터의 likelihood를 최대로 하는 베이지안망 구조를 찾는 문제는 NP-hard임이 알려져 있으므로, greedy search를 통한 근사해(approximate solution)를 구하는 방법이 주로 이용된다. 하지만 이러한 근사적 학습방법들도 데이터를 구성하는 변수들이 수천 - 수만에 이르는 경우, 방대한 계산량으로 인해 그 적용이 실질적으로 불가능하게 된다. 본 논문에서는 그러한 대규모 데이터에서 학습될 수 있는 계층적 베이지안망(hierarchical Bayesian network) 모델 및 그 학습방법을 제안하고, 그 가능성을 실험을 통해 보인다.

• 응용통계연구
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• 제27권6호
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• pp.975-989
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• 2014

연속적인 변수 선택과 계수 추정을 동시에 활용할 수 있다는 특성 때문에 LASSO (Tibshirani, 1996)와 Elastic Net (Zou와 Hastie, 2005)은 다양한 분야에서 활발하게 사용되고 있다. 조건부 라플라스와 이중 파레토 사전분포를 적용한 공액계층모형을 표현하였고, 각각의 사전분포에 대한 완전 조건 사후분포를 도출하였다. 제안된 사전분포를 적용한 벌점회귀모형을 비교하기 위한 모의 실험을 진행하였고, 예측정확도를 판단하기 위해 아시아 국가 실패(the collapse of governments in Asia)의 실제 데이터에 제안한 모형을 적용하였다.

• Communications for Statistical Applications and Methods
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• 제26권2호
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• pp.205-216
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• 2019

Diagnostic tests in medical fields detect or diagnose a disease with results measured by continuous or discrete ordinal data. The performance of a diagnostic test is summarized using the receiver operating characteristic (ROC) curve and the area under the curve (AUC). The diagnostic test is considered clinically useful if the outcomes in actually-positive cases are higher than actually-negative cases and the ROC curve is concave. In this study, we apply the stochastic ordering method in a Bayesian hierarchical model to estimate the proper ROC curve and AUC when the diagnostic test results are measured in discrete ordinal data. We compare the conventional binormal model and binormal model under stochastic ordering. The simulation results and real data analysis for breast cancer indicate that the binormal model under stochastic ordering can be used to estimate the proper ROC curve with a small bias even though the sample sizes were small or the sample size of actually-negative cases varied from actually-positive cases. Therefore, it is appropriate to consider the binormal model under stochastic ordering in the presence of large differences for a sample size between actually-negative and actually-positive groups.