Segmentation and intensity estimation of microarray images using a gamma-t mixture model

Baek, Jangsun,Son, Young Sook,McLachlan, Geoffrey J. Oxford University Press 2007 Bioinformatics Vol.23 No.4

<P><B>Motivation:</B> We present a new approach to the analysis of images for complementary DNA microarray experiments. The image segmentation and intensity estimation are performed simultaneously by adopting a two-component mixture model. One component of this mixture corresponds to the distribution of the background intensity, while the other corresponds to the distribution of the foreground intensity. The intensity measurement is a bivariate vector consisting of red and green intensities. The background intensity component is modeled by the bivariate gamma distribution, whose marginal densities for the red and green intensities are independent three-parameter gamma distributions with different parameters. The foreground intensity component is taken to be the bivariate <I>t</I> distribution, with the constraint that the mean of the foreground is greater than that of the background for each of the two colors. The degrees of freedom of this <I>t</I> distribution are inferred from the data but they could be specified in advance to reduce the computation time. Also, the covariance matrix is not restricted to being diagonal and so it allows for nonzero correlation between <I>R</I> and <I>G</I> foreground intensities. This gamma-<I>t</I> mixture model is fitted by maximum likelihood via the EM algorithm. A final step is executed whereby nonparametric (kernel) smoothing is undertaken of the posterior probabilities of component membership.</P><P>The main advantages of this approach are: (1) it enjoys the well-known strengths of a mixture model, namely flexibility and adaptability to the data; (2) it considers the segmentation and intensity simultaneously and not separately as in commonly used existing software, and it also works with the red and green intensities in a bivariate framework as opposed to their separate estimation via univariate methods; (3) the use of the three-parameter gamma distribution for the background red and green intensities provides a much better fit than the normal (log normal) or <I>t</I> distributions; (4) the use of the bivariate <I>t</I> distribution for the foreground intensity provides a model that is less sensitive to extreme observations; (5) as a consequence of the aforementioned properties, it allows segmentation to be undertaken for a wide range of spot shapes, including doughnut, sickle shape and artifacts.</P><P><B>Results:</B> We apply our method for gridding, segmentation and estimation to cDNA microarray real images and artificial data. Our method provides better segmentation results in spot shapes as well as intensity estimation than Spot and spotSegmentation R language softwares. It detected blank spots as well as bright artifact for the real data, and estimated spot intensities with high-accuracy for the synthetic data.</P><P><B>Availability:</B> The algorithms were implemented in Matlab. The Matlab codes implementing both the gridding and segmentation/estimation are available upon request.</P><P><B>Contact:</B> jbaek@chonnam.ac.kr</P><P><B>Supplementary information:</B> Supplementary material is available at <I>Bioinformatics</I> online.</P>

A Local Linear Kernel Estimator for Sparse Multinomial Data

Baek, Jangsun The Korean Statistical Society 1998 Journal of the Korean Statistical Society Vol.27 No.4

Burman (1987) and Hall and Titterington (1987) studied kernel smoothing for sparse multinomial data in detail. Both of their estimators for cell probabilities are sparse asymptotic consistent under some restrictive conditions on the true cell probabilities. Dong and Simonoff (1994) adopted boundary kernels to relieve the restrictive conditions. We propose a local linear kernel estimator which is popular in nonparametric regression to estimate cell probabilities. No boundary adjustment is necessary for this estimator since it adapts automatically to estimation at the boundaries. It is shown that our estimator attains the optimal rate of convergence in mean sum of squared error under sparseness. Some simulation results and a real data application are presented to see the performance of the estimator.

Mixtures of Factor Analyzers with Common Factor Loadings: Applications to the Clustering and Visualization of High-Dimensional Data

Jangsun Baek,McLachlan, Geoffrey J,Flack, Lloyd K IEEE 2010 IEEE transactions on pattern analysis and machine Vol.32 No.7

<P>Mixtures of factor analyzers enable model-based density estimation to be undertaken for high-dimensional data, where the number of observations n is not very large relative to their dimension p. In practice, there is often the need to further reduce the number of parameters in the specification of the component-covariance matrices. To this end, we propose the use of common component-factor loadings, which considerably reduces further the number of parameters. Moreover, it allows the data to be displayed in low--dimensional plots.</P>

Kernel Regression Estimation for Permutation Fixed Design Additive Models

Baek, Jangsun,Wehrly, Thomas E. The Korean Statistical Society 1996 Journal of the Korean Statistical Society Vol.25 No.4

Consider an additive regression model of Y on X = (X$_1$,X$_2$,. . .,$X_p$), Y = $sum_{j=1}^pf_j(X_j) + $\varepsilon$$, where $f_j$s are smooth functions to be estimated and $\varepsilon$ is a random error. If $X_j$s are fixed design points, we call it the fixed design additive model. Since the response variable Y is observed at fixed p-dimensional design points, the behavior of the nonparametric regression estimator depends on the design. We propose a fixed design called permutation fixed design, and fit the regression function by the kernel method. The estimator in the permutation fixed design achieves the univariate optimal rate of convergence in mean squared error for any p $\geq$ 2.

Goodness-of-Fit Test Using Local Maximum Likelihood Polynomial Estimator for Sparse Multinomial Data

Jangsun Baek 한국통계학회 2004 Journal of the Korean Statistical Society Vol.33 No.3

We consider the problem of testing cell probabilities in sparse multino- mial data. Aerts et al. (2000) presented T = Pk i=1fp i က E(p i )g2 as a test statistic with the local least square polynomial estimator p i , and derived its asymptotic distribution. The local least square estimator may produce negative estimates for cell probabilities. The local maximum likelihood poly- nomial estimator ^pi, however, guarantees positive estimates for cell proba- bilities and has the same asymptotic performance as the local least square estimator (Baek and Park, 2003). When there are cell probabilities with rel- atively much dierent sizes, the same contribution of the dierence between the estimator and the hypothetical probability at each cell in their test statis- tic would not be proper to measure the total goodness-of-t. We consider a Pearson type of goodness-of-t test statistic, T1 = Pk i=1f^pi က E(^pi)g2=pi instead, and show it follows an asymptotic normal distribution. Also we investigate the asymptotic normality of T2 = Pk i=1f^pi က E(^pi)g2 where the minimum expected cell frequency is very small.

Calculating credit limits with the one-factor asset model

Ko, Kwangyee,Baek, Jangsun Korean Data and Information Science Society 2018 한국데이터정보과학회지 Vol.29 No.4

In the current credit-risk system, a company's credit quality can be evaluated by a credit rating, but this does not determine its credit quantity. We define a firm's credit quantity as the firm's credit limit that can be provided to the firm based on the value of the firm's assets. Our purpose in this paper is to prevent an abnormal increase in credit exposure by managing a firm's total loan amount (TLA) within the credit limit granted based on the firm's asset value. We propose a one-factor asset model instead of the Merton's asset model and estimate the credit limit corresponding to the firm's credit rating from the one-factor asset model. We also developed a credit limit system with five credit limit grades based on estimates of credit limits to effectively apply credit limit policies to risk management. We show that reasonable credit limit management can substantially reduce the losses of financial institutions through empirical results.

Calculating credit limits with the one-factor asset model

Kwangyee Ko,Jangsun Baek 한국데이터정보과학회 2018 한국데이터정보과학회지 Vol.29 No.4

In the current credit-risk system, a company"s credit quality can be evaluated by a credit rating, but this does not determine its credit quantity. We define a firm"s credit quantity as the firm"s credit limit that can be provided to the firm based on the value of the firm"s assets. Our purpose in this paper is to prevent an abnormal increase in credit exposure by managing a firm"s total loan amount (TLA) within the credit limit granted based on the firm"s asset value. We propose a one-factor asset model instead of the Merton"s asset model and estimate the credit limit corresponding to the firm"s credit rating from the one-factor asset model. We also developed a credit limit system with five credit limit grades based on estimates of credit limits to effectively apply credit limit policies to risk management. We show that reasonable credit limit management can substantially reduce the losses of financial institutions through empirical results.

The local influence of LIU type estimator in linear mixed model

Zhang, Lili,Baek, Jangsun The Korean Data and Information Science Society 2015 한국데이터정보과학회지 Vol.26 No.2

In this paper, we study the local influence analysis of LIU type estimator in the linear mixed models. Using the method proposed by Shi (1997), the local influence of LIU type estimator in three disturbance models are investigated respectively. Furthermore, we give the generalized Cook's distance to assess the influence, and illustrate the efficiency of the proposed method by example.

비대칭 혼합모형과 요인분석자 혼합모형을 이용한 VaR 추정

고광이(Kwangyee Ko),백장선(Jangsun Baek) 한국데이터정보과학회 2018 한국데이터정보과학회지 Vol.29 No.3

투자위험을 관리해야하는 금융기관에서 다수의 투자수익으로 구성된 포트폴리오 VaR (Value-at-Risk)를 정확히 추정하는 것은 매우 중요하다. VaR 예측을 위한 투자수익의 분포는 종종 두꺼운 꼬리를 갖고 있거나 왜도나 첨도가 존재한다. 본 연구에서는 총투자수익률의 VaR를 추정하기 위하여 MSN (mixtures of skew-normal distribution), MSt (mixtures of skew-t distribution) 등 비대칭혼합모형 뿐만 아니라, 고차원 자료 분포의 모수추정에 보다 절약적인 요인분석자 모형인 MFA (mixtures of factor analyzers), MCFA (mixtures of common factor analyzers), MCtFA (mixtures of common t factor analyzers) 등이 고려되었다. 한국 코스피 시장의 회사주식 수익률 자료를 이용하여 실증 분석한 결과 고려된 혼합모형들이 VaR 추정에 있어서 모두 비슷한 성능을 보여주고 있으나, MFA 모형과 MCtFA 모형이 다른 모형들에 비해서 상대적으로 자료의 경험적 VaR에 조금 더 가까운 추정값을 도출하였다. It is very important to estimate VaR (Value-at-Risk) of the portfolio with many returns on investment for risk management. The distribution of returns has often thick tails, skewness or kurtosis. In order to estimate VaR of the total investment return, we consider not only mixture of skewed distributions models such as MSN (Mixtures of skew-normal distribution) and MSt (Mixtures of skew-t distribution), but also various parsimonious mixtures of factor analyzers models of MFA (Mixtures of factor analyzers), MCFA (Mixtures of common factor analyzers) and MCtFA (Mixtures of common skew-t factor analyzers). Application of the models to the KOSPI returns data showed that all models have the similar performance for estimating 1% - 5% VaR, but the estimates of MFA and MCtFA are more close to the empirical VaRs of the data.

기상자료를 이용한 마늘 생산량 추정

최성천,백장선,Choi, Sungchun,Baek, Jangsun 한국데이터정보과학회 2016 한국데이터정보과학회지 Vol.27 No.4

야외에서 재배되는 주요 채소류의 생산에 대한 기상변화의 영향력이 점차 커지고 있다. 기상변화로 인한 농작물 생산량의 변화는 공급과 수요의 불안정과 물가안정의 불안요소로 작용하고 있다. 본 논문에서는 패널회귀모형을 이용하여 기상상태에 따른 마늘의 생산량을 추정하였다. 2006년부터 2015년까지의 마늘 주산지 15곳의 10a당 마늘 생산량과 해당 지역의 기상자료를 사용하였다. 7가지 기상요인 (평균기온, 평균최저기온, 평균최고기온, 누적강수량, 누적일조시간, 평균상대습도, 평균지면온도)의 월별 (1월-12월)자료인 총 84개 기상변수중 다중회귀분석 단계선택방법을 통하여 7가지 기상변수를 선택하여 패널회귀모형에 사용하였다. 고정효과 모형과 확률효과 모형을 구분하는 하우스만 검정을 통하여 확률효과 모형으로 분석한 결과 평균최고기온 (1월), 누적강수량 (3월, 10월), 누적일조시간 (4월, 10월)등이 마늘 생산량 추정에 유의한 변수로 나타났다. 또한 연도별로 추정된 생산량 추정값의 추이가 실제 생산량과 동일한 추세를 보이고 있어 제안된 패널 회귀 모형이 잘 적합됨을 확인할 수 있다. Climate change affects the growth of crops which were planted especially in fields, and it becomes more important to use climate data to predict the yields of the major vagetables. The variation of the crop products caused by climate change is one of the significant factors for the discrepancy of the demand and supply, and leads to the price instability. In this paper, using a panel regression model, we predicted the garlic yields with the weather conditions of different regions. More specifically we used the panel data of the several climate variables for 15 main garlic production areas from 2006 to 2015. Seven variables (average temperature, average maximum temperature, average minimum temperature, average surface temperature, cumulative precipitation, average relative humidity, cumulative duration time of sunshine) for each month were considered, and most significant 7 variables were selected from the total 84 variables by the stepwise regression. The random effects model was chosen by the Hausman test. The average maximum temperature (January), the cumulative precipitation (March, October), the cumulative duration time of sunshine (April, October) were chosen among the variables as the significant climate variables of the model