• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.611-622
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• 2014

The inverse Weibull distribution (IWD) is the complementary Weibull distribution and plays an important role in many application areas. In Bayesian analysis, Soland's method can be considered to avoid computational complexities. One limitation of this approach is that parameters of interest are restricted to a finite number of values. This paper introduce nonparametric Bayesian estimator in the context of record statistics values from the exponentiated inverse Weibull distribution (EIWD). In stead of Soland's conjugate piror, stick-breaking prior is considered and the corresponding Bayesian estimators under the squared error loss function (quadratic loss) and LINEX loss function are obtained and compared with other estimators. The results may be of interest especially when only record values are stored.

• Communications for Statistical Applications and Methods
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• v.19 no.6
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• pp.885-898
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• 2012

In this paper, we consider Bayesian approaches to partially linear models, in which a regression function is represented by a semiparametric additive form of a parametric linear regression function and a nonparametric regression function. We make a comparative study on the performance of widely used Bayesian partially linear models in terms of empirical analysis. Specifically, we deal with three Bayesian methods to estimate the nonparametric regression function, one method using Fourier series representation, the other method based on Gaussian process regression approach, and the third method based on the smoothness of the function and differencing. We compare the numerical performance of three methods by the root mean squared error(RMSE). For empirical analysis, we consider synthetic data with simulation studies and real data application by fitting each of them with three Bayesian methods and comparing the RMSEs.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1129-1140
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• 2005

A nonparametric Bayesian method for calculating posterior probabilities of the multiple comparison problem on the parameters of several Geometric populations is presented. Bayesian multiple comparisons under two different prior/ likelihood combinations was studied by Gopalan and Berry(1998) using Dirichlet process priors. In this paper, we followed the same approach to calculate posterior probabilities for various hypotheses in a statistical experiment with a partition on the parameter space induced by equality and inequality relationships on the parameters of several geometric populations. This also leads to a simple method for obtaining pairwise comparisons of probability of successes. Gibbs sampling technique was used to evaluate the posterior probabilities of all possible hypotheses that are analytically intractable. A numerical example is given to illustrate the procedure.

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

• 한국데이터정보과학회:학술대회논문집
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• 2006.11a
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• pp.71-80
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• 2006

A nonparametric Bayesian multiple comparisons problem (MCP) for dependence parameters in I bivariate exponential populations is studied here. A simple method for pairwise comparisons of these parameters is also suggested. Here we extend the methodology studied by Gopalan and Berry (1998) using Dirichlet process priors. The family of Dirichlet process priors is applied in the form of baseline prior and likelihood combination to provide the comparisons. Computation of the posterior probabilities of all possible hypotheses are carried out through Markov Chain Monte Carlo method, namely, Gibbs sampling, due to the intractability of analytic evaluation. The whole process of MCP for the dependent parameters of bivariate exponential populations is illustrated through a numerical example.

• 한국데이터정보과학회:학술대회논문집
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• 2005.04a
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• pp.83-126
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• 2005

Single-index models have found applications in econometrics and biometrics, where multidimensional regression models are often encountered. Here we propose a nonparametric estimation approach that combines wavelet methods for non-equispaced designs with Bayesian models. We consider a wavelet series expansion of the unknown regression function and set prior distributions for the wavelet coefficients and the other model parameters. To ensure model identifiability, the direction parameter is represented via its polar coordinates. We employ ad hoc hierarchical mixture priors that perform shrinkage on wavelet coefficients and use Markov chain Monte Carlo methods for a posteriori inference. We investigate an independence-type Metropolis-Hastings algorithm to produce samples for the direction parameter. Our method leads to simultaneous estimates of the link function and of the index parameters. We present results on both simulated and real data, where we look at comparisons with other methods.

• YAKHAK HOEJI
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• v.40 no.1
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• pp.1-9
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• 1996

The purpose of this investigation was to determine pharmacokinetic parameters of gentamicin using nonlinear least square regression(NLSR) and Bayesian analysis in Korean normal volunteers and gastrointestinal surgical patients. Nonparametric expected maximum(NPEM) method for population pharmacokinetic parameters was used. Gentamicin was administered every 8 hours for 3 days by infusion over 30 minutes. The volume of distribution(V) and elimination rate constant(K) of gentamicin were $0.226{\pm}0.032,\;0.231{\pm}0.063L/Kg\;and\;0.357{\pm}0.024,\;0.337{\pm}0.041hr^{-1}$ for normal volunteers and gastrointestinal surgical patients using NLSR analysis. Population pharmacokinetic parameters, KS and VS were $0.00344{\pm}0.00049(hr{\cdot}ml/min/1.73m^2)^{-1}\;and\;0.214{\pm}0.0502L/Kg$ for gastrointestinal surgical patients using NPEM method. The V and K were $0.216{\pm}0.048L/Kg\;and\;0.336{\pm}0.043hr^{-1}$ for gastrointestinal surgical patients using Bayesian analysis. There were no differences in gentamicin pharmacokinetics between NLSR and Bayesian analysis in gastrointestinal surgical patient.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.1049-1068
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• 2014

Autoregressive models are used to analyze an univariate time series data; however, these methods can be inappropriate when a structural break appears in a time series since they assume that a trend is consistent. Threshold autoregressive models (popular regime-switching models) have been proposed to address this problem. Recently, the models have been extended to two regime-switching models with delay parameter. We discuss two regime-switching threshold autoregressive models from a Bayesian point of view. For a Bayesian analysis, we consider a parametric threshold autoregressive model and a nonparametric threshold autoregressive model using Dirichlet process prior. The posterior distributions are derived and the posterior inferences is performed via Markov chain Monte Carlo method and based on two Bayesian threshold autoregressive models. We present a simulation study to compare the performance of the models. We also apply models to gross domestic product data of U.S.A and South Korea.

• YAKHAK HOEJI
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• v.41 no.2
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• pp.195-202
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• 1997

The purpose of this study was to determine pharmacokinetic parameters of vancomycin using two point calculation(TPC) and Bayesian methods in 16 Korean normal volunteers and 15 g astric cancer patients. Nonparametric expected maximum(NPEM) algorithm for calculation of population pharmacokinetic parameter was used, and these parameters were applied for clinical pharmacokinetic parameters by Bayesian analysis. Vancomycin was administered 1.0g every 12 hrs for 3 days by IV infusion over 60 minutes. The volume of distribution(Vd), elimination rate constant(Kel) and total body clearance(CLt) of vancomycin in normal volunteers using TPC method were $0.34{\pm}0.06 L/kg,\; 0.19{\pm}0.01 hr^{-1}$ and $4.08 {\pm} 0.93 L/hr$, respectively, The Vd, Kel and CLt of vancomycin in gastric cancer patients using TPC method were $0.46 {\pm} 0.06 L/kg, 0.17{\pm}0.02 hr^{-1}$ and $4.84 {\pm} 0.57 L/hr$ respectively. There were significant differences(p<0.05) in Vd. Kel and CLt between normal volunteers and gastric cancer patients. Polpulation pharmacokinetic parameter, the slope(KS) of the relationship beetween Kel versus creatinine Clearance, and the Vd were $0.00157{\pm}0.00029(hr{\cdot}mL/min/1.73m^2)^{-1},\; 0.631 {\pm} 0.0036 L/kg$ in gastric cancer patients using NPEM algorithm respectively. The Vd and Kel were $0.63{\pm}0.005 L/kg, 0.15 {\pm}0.027 hr^{-1}$ for gastric cancer patients using Bayesian method. There were significant differences(p<0.05) in vancomycin pharmacokinetics between Bayesian and TPC methods. It is considered that the population parameter in the patient population is necessary for effective Bayesian method in clinical pharmacy practise.

• Communications for Statistical Applications and Methods
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• v.16 no.4
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• pp.713-722
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• 2009

The estimation of odds ratio and corresponding confidence intervals for case-control data have been done by traditional generalized linear models which assumed that the logarithm of odds ratio is linearly related to risk factors. We adapt a lower-dimensional approximation of Gu and Kim (2002) to provide a faster computation in nonparametric method for the estimation of odds ratio by allowing flexibility of the estimating function and its Bayesian confidence interval under the Bayes model for the lower-dimensional approximations. Simulation studies showed that taking larger samples with the lower-dimensional approximations help to improve the smoothing spline estimates of odds ratio in this settings. The proposed method can be used to analyze case-control data in medical studies.