• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.199-209
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• 2003

When a sampling theorem holds in wavelet subspaces, sampling expansions can be a good approximation to projection expansions. Even when the sampling theorem does not hold, the scaling function series with the usual coefficients replaced by sampled function values may also be a good approximation to the projection. We refer to such series as hybrid sampling series. For this series, we shall investigate the local convergence and analyze Gibbs phenomenon.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.181-193
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• 1998

The Shannon sampling series is the prototype of an interpolating series or sampling series. Also the Shannon wavelet is one of the protypes of wavelets. But the coefficients of the Shannon sampling series are different function values at the point of discontinuity, we analyze the Gibbs phenomenon for the Shannon sampling series. We also find a way to go around this overshoot effect.

• Journal of Animal Science and Technology
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• v.46 no.5
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• pp.719-728
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• 2004

The aims of this study were to estimate genetic parameters for carcass traits on Hanwoo(Korean Native Cattle) and to compare two different statistical algorithms for estimating genetic parameters. Data obtained from 1526 steers at Hanwoo Improvement Center and Hanwoo Improvement Complex Area from 1996 to 2001 were used for the analyses. The carcass traits considered in these studies were carcass weight, dressing percent, eye muscle area, backfat thickness, and marbling score. Estimated genetic parameters using EM-REML algorithm were compared to those by Bayesian inference via Gibbs Sampling to find out statistical properties. The estimated heritabilities of carcass traits by REML method were 0.28, 0.25, 0.35, 0.39 and 0.51, respectively and those by Gibbs Sampling method were 0.29, 0.25, 0.40, 0.42 and 0.54, respectively. This estimates were not significantly different, even though the estimated heritabilities by Gibbs Sampling method were higher than ones by REML method. Since the estimated statistics by REML method and Gibbs Sampling method were not significantly different in this study, it is inferred that both mothods could be efficiently applied for the analysis of carcass traits of cattle. However, further studies are demanded to define an optimal statistical method for handling large scale performance data.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.719-736
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• 2005

An understanding of Fourier series and their generalization is important for physics and engineering students, as much for mathematical and physical insight as for applications. Students are usually confused by the so-called Gibbs' phenomenon, an overshoot between a discontinuous function and its approximation by a Fourier series as the number of terms in the series becomes indefinitely large. In this paper we give short story of Gibbs phenomenon in chronological order.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.557-573
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• 2015

In this paper we develop a Bayesian inference for a multiplicative double seasonal autoregressive (DSAR) model by implementing a fast, easy and accurate Gibbs sampling algorithm. We apply the Gibbs sampling to approximate empirically the marginal posterior distributions after showing that the conditional posterior distribution of the model parameters and the variance are multivariate normal and inverse gamma, respectively. The proposed Bayesian methodology is illustrated using simulated examples and real-world time series data.

• The Korean Journal of Applied Statistics
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• v.7 no.1
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• pp.1-17
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• 1994

This article basically considers the calibration problem with censored data from the Bayesian point of view. The Gibbs sampling method is discussed to solve the difficulty encountered in computing the posterior distribution. Also presented is an approach for impementing the Gibbs sampling in actual data situation with the estimation procedures.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.463-482
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• 1994

In Bayesian analysis of randomized response models, the likelihood function does not combine tractably with typical priors for the parameters of interest, causing computational difficulties in posterior analysis of the parameters of interest. In this article, the difficulties are solved by introducing appropriate latent variables to the model and using the Gibbs sampling algorithm.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.255-266
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• 2007

A Bayesian estimation of the four-parameter gamma distribution is considered under the noninformative prior. The Bayesian estimators are obtained by the Gibbs sampling. The generation of the shape/power parameter and the power parameter in the Gibbs sampler is implemented using the adaptive rejection sampling algorithm of Gilks and Wild (1992). Also, the location parameter is generated using the adaptive rejection Metropolis sampling algorithm of Gilks, Best and Tan (1995). Finally, the simulation result is presented.

• The Korean Journal of Applied Statistics
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• v.16 no.2
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• pp.273-282
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• 2003

The problem of estimating the parameters of k-population Weibull distributions is discussed under the prior of ordered scale parameters. Parameters are estimated by the Gibbs sampling method. Since the conditional posterior distribution of the shape parameter in the Gibbs sampler is not log-concave, the shape parameter is generated by the adaptive rejection sampling. Finally, we applied this estimation methodology to the data discussed in Nelson (1970).

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.169-180
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• 1999

A Markov Chain Monte Carlo method with development of computation is used to be the software system reliability probability model. For Bayesian estimator considering computational problem and theoretical justification we studies relation Markov Chain with Gibbs sampling. Special case of GOS with Superposition for Goel-Okumoto and Weibull models using Gibbs sampling and Metropolis algorithm considered. In this paper discuss Bayesian computation and model selection using posterior predictive likelihood criterion. We consider in this paper data using method by Cox-Lewis. A numerical example with a simulated data set is given.