• Journal of Korean Institute of Industrial Engineers
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• v.42 no.4
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• pp.256-262
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• 2016

The Weibull is widely used in reliability analysis, and several studies have attempted to improve estimation of the distribution's parameters. least squares estimation (LSE) or Maximum likelihood estimation (MLE) are often used to estimate distribution parameters. However, it has been proven that Bayesian methods are more suitable for small sample sizes than LSE and MLE. In this work, the Weibull parameter estimation accuracy of LSE, MLE, and Bayesian method are compared for sample sets with 3 to 30 data points. The Bayesian method was most accurate for sample sizes under 25, and the accuracy of the Bayesian method was similar to LSE and MLE as the sample size increased.

• 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.27 no.6
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• pp.1621-1629
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• 2016

This paper studies Bayesian pooling for analysis of categorical data from small areas. Many surveys consist of categorical data collected on a contingency table in each area. Statistical inference for small areas requires considerable care because the subpopulation sample sizes are usually very small. Typically we use the hierarchical Bayesian model for pooling subpopulation data. However, the customary hierarchical Bayesian models may specify more exchangeability than warranted. We, therefore, investigate the effects of pooling in hierarchical Bayesian modeling for the contingency table from small areas. In specific, this paper focuses on the methods of direct or indirect pooling of categorical data collected on a contingency table in each area through Dirichlet priors. We compare the pooling effects of hierarchical Bayesian models by fitting the simulated data. The analysis is carried out using Markov chain Monte Carlo methods.

• Journal of the Korean Data and Information Science Society
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• v.20 no.6
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• pp.1191-1197
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• 2009

Most Bayesian approaches to model selection of wavelet analysis have drawbacks that computational cost is expensive to obtain accuracy for the fitted unknown function. To overcome the drawback, this article introduces loss functions which are criteria for level dependent threshold selection in wavelet based Bayesian methods with arbitrary size and regular design points. We demonstrate the utility of these criteria by four test functions and real data.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1465-1476
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• 2008

In recent years wavelet methods have been focused on block shrinkage or thresholding approaches to accounting for the sparseness of the wavelet representation for an unknown function. The block shrinkage or thresholding methods have been developed in both of classical methods and Bayesian methods. In this paper, we propose a Bayesian approach to selecting wavelet basis functions at each resolution level without MCMC procedure. Simulation study and an application are shown.

• Communications for Statistical Applications and Methods
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• v.30 no.3
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• pp.311-330
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• 2023

The present work describes simulation studies to compare the performances in terms of averaged mean squared error of bayesian wavelet shrinkage methods in estimating component curves from aggregated functional data. Five bayesian methods available in the literature were considered to be compared in the studies: The shrinkage rule under logistic prior, shrinkage rule under beta prior, large posterior mode (LPM) method, amplitude-scale invariant Bayes estimator (ABE) and Bayesian adaptive multiresolution smoother (BAMS). The so called Donoho-Johnstone test functions, logit and SpaHet functions were considered as component functions and the scenarios were defined according to different values of sample size and signal to noise ratio in the datasets. It was observed that the signal to noise ratio of the data had impact on the performances of the methods. An application of the methodology and the results to the tecator dataset is also done.

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.725-732
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• 2002

P-values are often perceived as measurements of degree of compatibility between the current data and the hypothesized model. In this paper, a new concept of Bayesian p-values is proposed and studied under the non-informative prior distributions, which can be thought as the Bayesian counterparts of the classical p-values in the sense of using the concept of significance level. The performances of the proposed Bayesian p-values are compared with those of the classical p-values through several examples.

• Communications for Statistical Applications and Methods
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• v.4 no.2
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• pp.465-471
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• 1997

This paper deals with the problems of obtaining some Bayesian and empirical Bayesian Predictive densities and prediction intervals of a future observation $X_{(\tau+\gamma)}$ in the Rayleigh distribution. Using an inverse gamma prior distribution, some prodictive densities and prodiction intervals are proposed and studied. Also the behaviors of the proposed results are examined via numerical examples.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.259-269
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• 1997

Bayesian inference for a record value statistics(RVS) model of nonhomogeneous Poisson process is considered. We seal with Bayesian inference for double exponential, Gamma, Rayleigh, Gumble RVS models using Gibbs sampling and Metropolis algorithm and also explore Bayesian computation and model selection.

• The KIPS Transactions:PartB
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• v.17B no.5
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• pp.381-388
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• 2010

Naive Bayesian learning has been widely used in many data mining applications, and it performs surprisingly well on many applications. However, due to the assumption that all attributes are equally important in naive Bayesian learning, the posterior probabilities estimated by naive Bayesian are sometimes poor. In this paper, we propose more fine-grained weighting methods, called value weighting, in the context of naive Bayesian learning. While the current weighting methods assign a weight to each attribute, we assign a weight to each attribute value. We investigate how the proposed value weighting effects the performance of naive Bayesian learning. We develop new methods, using gradient descent method, for both value weighting and feature weighting in the context of naive Bayesian. The performance of the proposed methods has been compared with the attribute weighting method and general Naive bayesian, and the value weighting method showed better in most cases.