• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.17-23
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• 2005

In this paper we consider the well-known semiparametric proportional hazards models for survival analysis. These models are usually used with few covariates and many observations (subjects). But, for a typical setting of gene expression data from DNA microarray, we need to consider the case where the number of covariates p exceeds the number of samples n. For a given vector of response values which are times to event (death or censored times) and p gene expressions(covariates), we address the issue of how to reduce the dimension by selecting the significant genes. This approach enables us to estimate the survival curve when n ${\ll}$p. In our approach, rather than fixing the number of selected genes, we will assign a prior distribution to this number. The approach creates additional flexibility by allowing the imposition of constraints, such as bounding the dimension via a prior, which in effect works as a penalty To implement our methodology, we use a Markov Chain Monte Carlo (MCMC) method. We demonstrate the use of the methodology to diffuse large B-cell lymphoma (DLBCL) complementary DNA (cDNA) data and Breast Carcinomas data.

• Genomics & Informatics
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• v.20 no.1
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• pp.8.1-8.14
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• 2022

Despite the success of recent genome-wide association studies investigating longitudinal traits, a large fraction of overall heritability remains unexplained. This suggests that some of the missing heritability may be accounted for by gene-gene and gene-time/environment interactions. In this paper, we develop a Bayesian variable selection method for longitudinal genetic data based on mixed models. The method jointly models the main effects and interactions of all candidate genetic variants and non-genetic factors and has higher statistical power than previous approaches. To account for the within-subject dependence structure, we propose a grid-based approach that models only one fixed-dimensional covariance matrix, which is thus applicable to data where subjects have different numbers of time points. We provide the theoretical basis of our Bayesian method and then illustrate its performance using data from the 1000 Genome Project with various simulation settings. Several simulation studies show that our multivariate method increases the statistical power compared to the corresponding univariate method and can detect gene-time/ environment interactions well. We further evaluate our method with different numbers of individuals, variants, and causal variants, as well as different trait-heritability, and conclude that our method performs reasonably well with various simulation settings.

• Proceedings of the Korea Water Resources Association Conference
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• 2022.05a
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• pp.137-137
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• 2022

Evaluating interpolated rainfall uncertainty of hydrological models caused by different interpolation methods for basins where can not fully collect rainfall data are necessary. In this study, the adaptive MCMC method under effects of ILFs was used to analyze the interpolated rainfall uncertainty of the SURR model for Gunnam basin, Korea. Three events were used to calibrate and one event was used to validate the posterior distributions of unknown parameters. In this work, the performance of four ILFs on uncertainty of interpolated rainfall was assessed. The indicators of p_factor (percentage of observed streamflow included in the uncertainty interval) and r_factor (the average width of the uncertainty interval) were used to evaluate the uncertainty of the simulated streamflow. The results showed that the uncertainty bounds illustrated the slight differences from various ILFs. The study confirmed the importance of the likelihood function selection in the application the adaptive Bayesian MCMC method to the uncertainty assessment of the SURR model caused by interpolated rainfall.

• The Korean Journal of Applied Statistics
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• v.24 no.4
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• pp.677-693
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• 2011

In this paper, we consider Bayesian approaches to zero inflated Poisson model, one of the popular models to analyze zero inflated count data. To generate posterior samples, we deal with a Markov Chain Monte Carlo method using a Gibbs sampler and an exact sampling method using an Inverse Bayes Formula(IBF). Posterior sampling algorithms using two methods are compared, and a convergence checking for a Gibbs sampler is discussed, in particular using posterior samples from IBF sampling. Based on these sampling methods, a real data analysis is performed for Trajan data (Marin et al., 1993) and our results are compared with existing Trajan data analysis. We also discuss model selection issues for Trajan data between the Poisson model and zero inflated Poisson model using various criteria. In addition, we complement the previous work by Rodrigues (2003) via further data analysis using a hierarchical Bayesian model.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.65-83
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• 2022

Although various statistical methods have been developed to map time-dependent genetic factors, most identified genetic variants can explain only a small portion of the estimated genetic variation in longitudinal traits. Gene-gene and gene-time/environment interactions are known to be important putative sources of the missing heritability. However, mapping epistatic gene-gene interactions is extremely difficult due to the very large parameter spaces for models containing such interactions. In this paper, we develop a Gaussian process (GP) based nonparametric Bayesian variable selection method for longitudinal data. It maps multiple genetic markers without restricting to pairwise interactions. Rather than modeling each main and interaction term explicitly, the GP model measures the importance of each marker, regardless of whether it is mostly due to a main effect or some interaction effect(s), via an unspecified function. To improve the flexibility of the GP model, we propose a novel grid-based method for the within-subject dependence structure. The proposed method can accurately approximate complex covariance structures. The dimension of the covariance matrix depends only on the number of fixed grid points although each subject may have different numbers of measurements at different time points. The deviance information criterion (DIC) and the Bayesian predictive information criterion (BPIC) are proposed for selecting an optimal number of grid points. To efficiently draw posterior samples, we combine a hybrid Monte Carlo method with a partially collapsed Gibbs (PCG) sampler. We apply the proposed GP model to a mouse dataset on age-related body weight.

• Journal of Applied Reliability
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• v.1 no.2
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• pp.183-192
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• 2001

Jelinski-Moranda model and modified Jelinski-Moranda model in software reliability are studied and we consider maximum likelihood estimator and Bayes estimates of the number of faults and the fault-detection rate per fault. A gibbs sampling approach is employed to compute the Bayes estimates, future survival function is examined. Model selection based on prequential likelihood of the conditional predictive ordinates. A numerical example with simulated data set is given.

• Journal of the Korean Statistical Society
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• v.30 no.1
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• pp.163-178
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• 2001

We consider the experimental design problem of selecting values of design variables x for observation of a response y that depends on x and on model parameters $\theta$. The form of the dependence may be quite general, including all linear and nonlinear modeling situations. The goal of the design selection is to efficiently estimate functions of $\theta$. Three new criteria for selecting design points x are presented. The criteria generalized the usual Bayesian optimal design criteria to situations n which the prior distribution for $\theta$ amy be uncertain. We assume that there are several possible prior distributions,. The new criteria are applied to the nonlinear problem of designing to estimate the turning point of a quadratic equation. We give both analytic and computational results illustrating the robustness of the optimal designs based on the new criteria.

• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.189-204
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• 2021

In a regression analysis, a single best model is usually selected among several candidate models. However, it is often useful to combine several candidate models to achieve better performance, especially, in the prediction viewpoint. Model combining methods such as stacking and Bayesian model averaging (BMA) have been suggested from the perspective of averaging candidate models. When the candidate models include a true model, it is expected that BMA generally gives better performance than stacking. On the other hand, when candidate models do not include the true model, it is known that stacking outperforms BMA. Since stacking and BMA approaches have different properties, it is difficult to determine which method is more appropriate under other situations. In particular, it is not easy to find research papers that compare stacking and BMA when regression model assumptions are violated. Therefore, in the paper, we compare the performance among model averaging methods as well as a single best model in the linear regression analysis when standard linear regression assumptions are violated. Simulations were conducted to compare model averaging methods with the linear regression when data include outliers and data do not include them. We also compared them when data include errors from a non-normal distribution. The model averaging methods were applied to the water pollution data, which have a strong multicollinearity among variables. Simulation studies showed that the stacking method tends to give better performance than BMA or standard linear regression analysis (including the stepwise selection method) in the sense of risks (see (3.1)) or prediction error (see (3.2)) when typical linear regression assumptions are violated.

• Journal of the Korean Statistical Society
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• v.27 no.4
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• pp.407-420
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• 1998

This paper is concerned with selecting covariates to be included in building linear random effects models designed to analyze clustered response normal data. It is based on a Bayesian approach, intended to propose and develop a procedure that uses probabilistic considerations for selecting premising subsets of covariates. The approach reformulates the linear random effects model in a hierarchical normal and point mass mixture model by introducing a set of latent variables that will be used to identify subset choices. The hierarchical model is flexible to easily accommodate sign constraints in the number of regression coefficients. Utilizing Gibbs sampler, the appropriate posterior probability of each subset of covariates is obtained. Thus, In this procedure, the most promising subset of covariates can be identified as that with highest posterior probability. The procedure is illustrated through a simulation study.

• The Korean Journal of Applied Statistics
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• v.35 no.2
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• pp.217-227
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• 2022

Quantile regression is widely used in many fields based on the advantage of providing an efficient tool for examining complex information latent in variables. However, modern large-scale and high-dimensional data makes it very difficult to estimate the quantile regression model due to limitations in terms of computation time and storage space. Divide-and-conquer is a technique that divide the entire data into several sub-datasets that are easy to calculate and then reconstruct the estimates of the entire data using only the summary statistics in each sub-datasets. In this paper, we studied on a variable selection method using Bayes information criteria by applying the divide-and-conquer technique to the penalized quantile regression. When the number of sub-datasets is properly selected, the proposed method is efficient in terms of computational speed, providing consistent results in terms of variable selection as long as classical quantile regression estimates calculated with the entire data. The advantages of the proposed method were confirmed through simulation data and real data analysis.