• 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.

• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.63-75
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• 2002

Most attempts at Bayesian analysis of neural networks involve hierarchical modeling. We believe that similar results can be obtained with simpler models that require less computational effort, as long as appropriate restrictions are placed on parameters in order to ensure propriety of posterior distributions. In particular, we adopt a model first introduced by Lee (1999) that utilizes an improper prior for all parameters. Straightforward Gibbs sampling is possible, with the exception of the bias parameters, which are embedded in nonlinear sigmoidal functions. In addition to the problems posed by nonlinearity, direct sampling from the posterior distributions of the bias parameters is compounded due to the duplication of hidden nodes, which is a source of multimodality. In this regard, we focus on sampling from the marginal posterior distribution of the bias parameters with Markov chain Monte Carlo methods that combine traditional Metropolis sampling with a slice sampler described by Neal (1997, 2001). The methods are illustrated with data examples that are largely confined to the analysis of nonparametric regression models.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1391-1396
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• 2008

In this paper, we consider two components system which the lifetimes have Marshall and Olkin's bivariate exponential model with bivariate type I censored data. We propose a Bayesian independent test procedure for above model using fractional Bayes factor method by O'Hagan based on improper prior distributions. And we compute the fractional Bayes factor and the posterior probabilities for the hypotheses, respectively. Also we select a hypothesis which has the largest posterior probability. Finally a numerical example is given to illustrate our Bayesian testing procedure.

• The Korean Journal of Applied Statistics
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• v.11 no.1
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• pp.97-111
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• 1998

This paper suggests a Bayesian method for testing first-order markov correlation among linear regression disturbances. As a Bayesian test criterion, Bayes factor is derived in the form of generalized Savage-Dickey density ratio that is easily estimated by means of posterior simulation via Gibbs sampling scheme. Performance of the Bayesian test is evaluated and examined based upon a Monte Carlo experiment and an empirical data analysis. Efficiency of the posterior simulation is also examined.

• The Korean Journal of Applied Statistics
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• v.22 no.4
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• pp.687-695
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• 2009

The Bayesian multiple change-point estimation has been applied to the daily means of ozone and PM10 data in Seoul for the period 1999. We focus on the detection of multiple change-points in the ozone and PM10 bivariate vectors by evaluating the posterior probabilities and Bayesian information criterion(BIC) using the stochastic approximation Monte Carlo(SAMC) algorithm. The result gives 5 change-points of mean vectors of ozone and PM10, which are related with the seasonal characteristics.

• Journal of the Korean Statistical Society
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• v.34 no.2
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• pp.85-98
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• 2005

A Bayesian analysis for the product of different powers of k independent Poisson rates, written ${\theta}$, is developed. This is done by considering a prior for ${\theta}$ that satisfies the differential equation due to Tibshirani and induces a proper posterior distribution. The Gibbs sampling procedure utilizing the rejection method is suggested for the posterior inference of ${\theta}$. The procedure is straightforward to specify distributionally and to implement computationally, with output readily adapted for required inference summaries. A salient feature of the procedure is that it provides a unified method for inferencing ${\theta}$ with any type of powers, and hence it solves all the existing problems (in inferencing ${\theta}$) simultaneously in a completely satisfactory way, at least within the Bayesian framework. In two examples, practical applications of the procedure is described.

• Communications for Statistical Applications and Methods
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• v.19 no.5
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• pp.705-720
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• 2012

In this paper, we introduce a hierarchical Bayesian model to simultaneously estimate the thresholds of each 6 cities. It was noted in the literature there was a dramatic increases in the number of deaths if the mean temperature passes a certain value (that we call a threshold). We estimate the difference of mortality before and after the threshold. For the hierarchical Bayesian analysis, some proper prior distribution of parameters and hyper-parameters are assumed. By combining the Gibbs and Metropolis-Hastings algorithm, we constructed a Markov chain Monte Carlo algorithm and the posterior inference was based on the posterior sample. The analysis shows that the estimates of the threshold are located at $25^{\circ}C{\sim}29^{\circ}C$ and the mortality around the threshold changes from -1% to 2~13%.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.589-598
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• 1999

Classification errors are included in sampling -with -re-placement model where items are sampled from a Bernoulli process. Bayesian imperfect inspection model is considered. In addition con-jugate prior and predctive densities for imperfect inspection model are obtained.

• 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 Bulletin of The Korean Astronomical Society
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• v.41 no.2
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• pp.62.2-62.2
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• 2016

We present a newly developed algorithm based on a Bayesian method for 2D tilted-ring analysis of disk galaxies which operates on velocity fields. Compared to the conventional ones based on a chi-squared minimisation procedure, this new Bayesian-based algorithm less suffers from local minima of the model parameters even with high multi-modality of their posterior distributions. Moreover, the Bayesian analysis implemented via Markov Chain Monte Carlo (MCMC) sampling only requires broad ranges of posterior distributions of the parameters, which makes the fitting procedure fully automated. This feature is essential for performing kinematic analysis of an unprecedented number of resolved galaxies from the upcoming Square Kilometre Array (SKA) pathfinders' galaxy surveys. A standalone code, the so-called '2D Bayesian Automated Tilted-ring fitter' (2DBAT) that implements the Bayesian fits of 2D tilted-ring models is developed for deriving rotation curves of galaxies that are at least marginally resolved (> 3 beams across the semi-major axis) and moderately inclined (20 < i < 70 degree). The main layout of 2DBAT and its performance test are discussed using sample galaxies from Australia Telescope Compact Array (ATCA) observations as well as artificial data cubes built based on representative rotation curves of intermediate-mass and massive spiral galaxies.