• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.417-426
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• 2001

This paper addresses the nonparametric Bayesian estimation for the exponential populations under type II censoring. The Dirichlet process prior is used to provide nonparametric Bayesian estimates of parameters of exponential populations. In the past, there have been computational difficulties with nonparametric Bayesian problems. This paper solves these difficulties by a Gibbs sampler algorithm. This procedure is applied to a real example and is compared with a classical estimator.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.111-119
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• 2007

In this paper, we develop a nonparametric Bayesian methodology of estimating an unknown distribution function F at the given survival time with current status data under the assumption of Dirichlet process prior on F. We compare our algorithm with the nonparametric maximum likelihood estimator through application to simulated data and real data.

• 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.

• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.1-16
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• 2002

Since changepoint identification is important in many data analysis problem, we wish to make inference about the locations of one or more changepoints of the sequence. We consider the Bayesian nonparameteric inference for multiple changepoint problem using a Bayesian segmentation procedure proposed by Yang and Kuo (2000). A mixture of products of Dirichlet process is used as a prior distribution. To decide whether there exists a single change or not, our approach depends on nonparametric Bayesian Schwartz information criterion at each step. We discuss how to choose the precision parameter (total mass parameter) in nonparametric setting and show that the discreteness of the Dirichlet process prior can ha17e a large effect on the nonparametric Bayesian Schwartz information criterion and leads to conclusions that are very different results from reasonable parametric model. One example is proposed to show this effect.

• Communications for Statistical Applications and Methods
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• v.31 no.3
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• pp.323-336
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• 2024

The accurate forecasting of insurance claims is a critical component for insurers' risk management decisions. Hierarchical Bayesian parametric (BP) models can be used for health insurance claims forecasting, but they are unsatisfactory to describe the claims distribution. Therefore, Bayesian nonparametric (BNP) models can be a more suitable alternative to deal with the complex characteristics of the health insurance claims distribution, including heavy tails, skewness, and multimodality. In this study, we apply both a BP model and a BNP model to predict group health claims using simulated and real-world data for a private life insurer in Indonesia. The findings show that the BNP model outperforms the BP model in terms of claims prediction accuracy. Furthermore, our analysis highlights the flexibility and robustness of BNP models in handling diverse data structures in health insurance claims.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.445-466
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• 2016

Nonparametric Bayesian methods have seen rapid and sustained growth over the past 25 years. We present a gentle introduction to the methods, motivating the methods through the twin perspectives of consistency and false consistency. We then step through the various constructions of the Dirichlet process, outline a number of the basic properties of this process and move on to the mixture of Dirichlet processes model, including a quick discussion of the computational methods used to fit the model. We touch on the main philosophies for nonparametric Bayesian data analysis and then reanalyze a famous data set. The reanalysis illustrates the concept of admissibility through a novel perturbation of the problem and data, showing the benefit of shrinkage estimation and the much greater benefit of nonparametric Bayesian modelling. We conclude with a too-brief survey of fancier nonparametric Bayesian methods.

• 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.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.427-434
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• 2001

In this paper, we consider the nonparametric Bayesian approach to the multiple comparisons problem for I Poisson populations using Dirichlet process priors. We describe Gibbs sampling algorithm for calculating posterior probabilities for the hypotheses and calculate posterior probabilities for the hypotheses using Markov chain Monte Carlo. Also we provide a numerical example to illustrate the developed numerical technique.

• 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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• 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.