• 대한의용생체공학회:학술대회논문집
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• 대한의용생체공학회 1997년도 춘계학술대회
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• pp.279-282
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• 1997

Bayesian reconstruction methods for emission computed tomography have been a topic of interest in recent years, partly because they allow for the introduction of prior information into the reconstruction problem. Early formulations incorporated priors that imposed simple spatial smoothness constraints on the underlying object using Gibbs priors in the form of four-nearest or eight-nearest neighbors. While these types of priors, known as "membrane" priors, are useful as stabilizers in otherwise unstable ML-EM reconstructions, more sophisticated prior models are needed to model underlying source distributions more accurately. In this work, we investigate whether the "thin plate" model has advantages over the simple Gibbs smoothing priors mentioned above. To test and compare quantitative performance of the reconstruction algorithms, we use Monte Carlo noise trials and calculate bias and variance images of reconstruction estimates. The conclusion is that the thin plate prior outperforms the membrane prior in terms of bias and variance.

• Journal of the Korean Statistical Society
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• 제36권1호
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• pp.77-91
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• 2007

This paper considers development of noninformative priors for the familial data when the families have equal number of offspring. Several noninformative priors including the widely used Jeffreys' prior as well as the different reference priors are derived. Also, a simultaneously-marginally-probability-matching prior is considered and probability matching priors are derived when the parameter of interest is inter- or intra-class correlation coefficient. The simulation study implemented by Gibbs sampler shows that two-group reference prior is slightly edge over the others in terms of coverage probability.

• Asian-Australasian Journal of Animal Sciences
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• 제14권8호
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• pp.1051-1056
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• 2001

Data for teat number for Landrace (L), Yorkshire (Y), crossbred of Landrace and Yorkshire (LY), and crossbred of Landrace, Yorkshire and Chinese indigenous Min Pig (LYM) were analyzed using Gibbs sampling. In Bayesian inference, flat priors and some informative priors were used to examine their influence on posterior estimates. The posterior mean estimates of heritabilities with flat priors were $0.661{\pm}0.035$ for L, $0.540{\pm}0.072$ for Y, $0.789{\pm}0.074$ for LY, and $0.577{\pm}0.058$ for LYM, and they did not differ (p>0.05) from their corresponding estimates of REML. When inverse Gamma densities for variance components were used as priors with the shape parameter of 4, the posterior estimates were still corresponding (p>0.05) to REML estimates and mean estimates using Gibbs sampling with flat priors. However, when the inverse Gamma densities with the shape parameter of 10 were utilized, some posterior estimates differed (p<0.10) from REML estimates and/or from other Gibbs mean estimates. The use of moderate degree of belief was influential to the posterior estimates, especially for Y and for LY where data sizes were small. When the data size is small, REML estimates of variance components have unknown distributions. On the other hand, Bayesian approach gives exact posterior densities of variance components. However, when the data size is small and prior knowledge is lacked, researchers should be careful with even moderate priors.

• 한국신뢰성학회:학술대회논문집
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• 한국신뢰성학회 2000년도 추계학술대회
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• pp.411-411
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• 2000

Consider the problem of estimating the reliability of a multicomponent stress-strength system which functions if at least r of the k identical components simultaneously function. All stresses and strengths are assumed to be independent random variables with two parameter Weibull distributions. First, we derive reference priors and probability matching priors which are noninformative priors. We next investigate sufficient conditions for propriety of posteriors under reference priors and probability matching priors. Finally, we provide, using these priors, some numerical results for Bayes estimates of the reliability by applying Gibbs sampling technique.

• Communications for Statistical Applications and Methods
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• 제7권1호
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• pp.165-178
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• 2000

Bayesian methods are considered for the multiple caputure-recapture data. Reference priors are developed for such model and sampling-based approach through Gibbs sampler is used for inference from posterior distributions. Furthermore approximate Bayes factors are obtained for model selection between trap and nontrap response models. Finally one methodology is implemented for a capture-recapture model in generated data and real data.

• 대한의용생체공학회:의공학회지
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• 제19권2호
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• pp.133-142
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• 1998

Bayesian SPECT 영상재구성에 있어서 정교한 형태의 사전정보를 사용할 경우 bias 및 variance와 같은 통계적 차원에서의 정량적 성능을 향상시킬 수 있다. 특히, "thin plate" 와 같은 고차의 smoothing 사전정보는 "membrane"과 같은 일반적인 다른 사전 정보에 비해 bias를 개선시키는 것으로 알려져 있다. 그러나, 이와 같은 장점은 영상재구성 알고리즘에 내재하는 hyperparameters의 값을 최적으로 선택하였을 경우에만 적용된다. 본 연구에서는 thin plate와 membrane의 두가지 대표적인 사전정보를 포함하는 영상재구성 알고리즘의 정량적 성능에 대해 집중 고찰한다. 즉, 알고리즘에 내재하는 hyperparameters 가 통계적 차원에서 bias와 variance에 어떠한 영향을 미치는지 관찰한다. 실험에서 Monte Carlo noise trials를 사용하여 bias와 variance를 계산하며, 각 결과를 ML-EM 및 filtered backprojection으로부터 얻어진 bias 및 variance와 비교한다. 결론적으로 thin plate와 같은 고차의 사전정보는 hyperparameters의 선택에 민감하지 않으며, hyperparameters 값의 전 범위에 걸쳐 bias를 개선시킴을 보인다. 걸쳐 bias를 개선시킴을 보인다.

• Journal of the Korean Statistical Society
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• 제23권2호
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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.

• Journal of the Korean Statistical Society
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• 제33권2호
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• pp.169-189
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• 2004

Under the assumption of default priors, such as noninformative priors, Bayesian model determination and parameter estimation of regression models with stationary and invertible ARMA errors are developed under exact full likelihoods. The default Bayes factors, the fractional Bayes factor (FBF) of O'Hagan (1995) and the arithmetic intrinsic Bayes factors (AIBF) of Berger and Pericchi (1996a), are used as tools for the selection of the Bayesian model. Bayesian estimates are obtained by running the Metropolis-Hastings subchain in the Gibbs sampler. Finally, the results of numerical studies, designed to check the performance of the theoretical results discussed here, are presented.

• Communications for Statistical Applications and Methods
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• 제10권3호
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• pp.981-996
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• 2003

Bayesian inference is considered for switching mean models with the ARMA errors. We use noninformative improper priors or uniform priors. The fractional Bayes factor of O'Hagan (1995) is used as the Bayesian tool for detecting the existence of a single change or multiple changes and the usual Bayes factor is used for identifying the orders of the ARMA error. Once the model is fully identified, the Gibbs sampler with the Metropolis-Hastings subchains is constructed to estimate parameters. Finally, we perform a simulation study to support theoretical results.

• Journal of the Korean Data and Information Science Society
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• 제18권2호
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• pp.553-560
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• 2007

In this paper, we consider two components system which lifetimes have Freund's bivariate exponential model with equal failure rates. We propose Bayesian multiple comparisons procedure for the failure rates of I Freund's bivariate exponential populations based on Dirichlet process priors(DPP). The family of DPP is applied in the form of baseline prior and likelihood combination to provide the comparisons. Computation of the posterior probabilities of all possible hypotheses are carried out through Markov Chain Monte Carlo(MCMC) method, namely, Gibbs sampling, due to the intractability of analytic evaluation. The whole process of multiple comparisons problem for the failure rates of bivariate exponential populations is illustrated through a numerical example.