• Journal of Korean Society for Quality Management
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• v.26 no.1
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• pp.143-160
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• 1998

This article is concerned with the selection of subsets of predictor variables to be included in bulding the binary response logistic regression model. It is based on a Bayesian aproach, intended to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets. This procedure reformulates the logistic regression setup in a hierarchical normal mixture model by introducing a set of hyperparameters that will be used to identify subset choices. It is done by use of the fact that cdf of logistic distribution is a, pp.oximately equivalent to that of $t_{(8)}$/.634 distribution. The a, pp.opriate posterior probability of each subset of predictor variables is obtained by the Gibbs sampler, which samples indirectly from the multinomial posterior distribution on the set of possible subset choices. Thus, in this procedure, the most promising subset of predictors can be identified as that with highest posterior probability. To highlight the merit of this procedure a couple of illustrative numerical examples are given.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.27-40
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• 2022

In this paper, the focus on the removal noise in the binary image based on the variational Bayesian method with the Ising model. The observation and the latent variable are the degraded image and the original image, respectively. The posterior distribution is built using the Markov random field and the Ising model. Estimating the posterior distribution is the same as reconstructing a degraded image. MCMC and variational Bayesian inference are two methods for estimating the posterior distribution. However, for the sake of computing efficiency, we adapt the variational technique. When the image is restored, the iterative method is used to solve the recursive problem. Since there are three model parameters in this paper, restoration is implemented using the VECM algorithm to find appropriate parameters in the current state. Finally, the restoration results are shown which have maximum peak signal-to-noise ratio (PSNR) and evidence lower bound (ELBO).

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.395-411
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• 2005

In this paper, we develop the Jeffreys' prior, reference prior and the the probability matching priors for the difference of intraclass correlation coefficients in familial data. e prove the sufficient condition for propriety of posterior distributions. Using marginal posterior distributions under those noninformative priors, we compare posterior quantiles and frequentist coverage probability.

• Journal of the Korean Mathematical Society
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• v.61 no.5
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• pp.875-898
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• 2024

This study estimates the true price of an asset and finds the optimal bid/ask prices for market makers. We provide a novel state-space model based on the exponential Ornstein-Uhlenbeck volatility and the Heston models with Gaussian noise, where the traded price and volume are available, but the true price is not observable. An objective of this study is to use Bayesian filtering to estimate the posterior distribution of the true price, given the traded price and volume. Because the posterior density is intractable, we employ the guided particle filtering algorithm, with which adaptive rejection metropolis sampling is used to generate samples from the density function of an unknown distribution. Given a simulated sample path, the posterior expectation of the true price outperforms the traded price in estimating the true price in terms of both the mean absolute error and root-mean-square error metrics. Another objective is to determine the optimal bid/ask prices for a market maker. The profit-and-loss of the market maker is the difference between the true price and its bid/ask prices multiplied by the traded volume or bid/ask size of the market maker. The market maker maximizes the expected utility of the PnL under the posterior distribution. We numerically calculate the optimal bid/ask prices using the Monte Carlo method, finding that its spread widens as the market maker becomes more risk-averse, and the bid/ask size and the level of uncertainty increase.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.1069-1076
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• 2014

Rainfall weather patterns have changed due to global warming and sudden heavy rainfalls have become more frequent. Economic loss due to heavy rainfall has increased. We study the generalized Pareto distribution for modelling rainfall in Seoul based on data from 1973 to 2008. We use several priors including Jeffrey's noninformative prior and Gibbs sampling method to derive Bayesian posterior predictive distributions. The probability of heavy rainfall has increased over the last ten years based on estimated posterior predictive distribution.

• Journal of Applied Reliability
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• v.17 no.3
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• pp.188-196
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• 2017

Purpose: The purpose of this research is to determine optimal replacement age using non-informative prior information and Bayesian method. Methods: We propose a novel approach using Bayesian method to determine the optimal replacement age in block replacement policy by defining the prior probability with data on failure time and repair time. The Marcov Chain Monte Carlo simulation is used to investigate the asymptotic distribution of posterior parameters. Results: An optimal replacement age of block replacement policy is determined which minimizes cost and nonoperating time when no information on prior distribution of parameters is given. Conclusion: We find the posterior distribution of parameters when lack of information on prior distribution, so that the optimal replacement age which minimizes the total cost and maximizes the total values is determined.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09b
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• pp.45-48
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• 2003

We propose some properties of Bayesian fuzzy hypotheses testing by revision for prior possibility distribution and posterior possibility distribution using weighted fuzzy hypotheses H$\sub$0/($\theta$) versus H$_1$($\theta$) on $\theta$ with loss function.

• Communications for Statistical Applications and Methods
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• v.18 no.3
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• pp.295-300
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• 2011

The Bayesian nonparametric estimation of two uniformly stochastically ordered distributions is studied. We propose a restricted Dirichlet Process. Among many types of restriction we consider only uniformly stochastic ordering in this paper since the computation of integrals is relatively easy. An explicit expression of the posterior distribution is given. When square loss function is used the posterior distribution can be obtained by easy integration using some computer program such as Mathematica.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.647-654
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• 2003

Bayesian probability models for finite populations are considered assuming so-called the super-population. We find the posterior distribution of population mean by a new approach, using the concept of pivotal quantity for the small sample case. A large sample theory is also treated throught the concept of asymptotically pivotal quantity.

• Journal of the Korean Statistical Society
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• v.16 no.2
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• pp.92-101
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• 1987

Our interest is to access in some way teh relative odds or probability that a multivariate observation Z belongs to one of k multivariate normal populations with unequal covariance matrices. We derived the empirical Bayes posterior odds ratio for the classification rule when population parameters are unknown. It is a generalization of the posterior odds ratio suggested by Gelsser (1964). The classification rule does not have complicated distribution theory which a large variety of techniques from the sampling viewpoint have. The proposed posterior odds ratio is compared to the Gelsser's posterior odds ratio through a Monte Carlo study. The results show that the empiricla Bayes posterior odds ratio, in general, performs better than the Gelsser's. Especially, for large dimension of Z and small training sample, the performance is prominent.