• Journal of the Korean Data and Information Science Society
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• 제26권1호
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• pp.243-253
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• 2015

In this paper, we develop the noninformative priors for the common shape parameter of several inverse Gaussian distributions. Specially, we want to develop noninformative priors which satisfy certain objective criterion. The probability matching priors and reference priors of the common shape parameter will be developed. It turns out that the second order matching prior does not exist. The reference priors satisfy the first order matching criterion, but Jeffrey's prior is not the first order matching prior. We showed that the proposed reference prior matches the target coverage probabilities in a frequentist sense through simulation study, and an example based on real data is given.

• Journal of the Korean Data and Information Science Society
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• 제15권4호
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• pp.981-992
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• 2004

In this paper, we develop the noninformative priors for the common scale parameter in the inverse gaussian distributions. We developed the first and second order matching priors. Next we revealed that the second order matching prior satisfies a HPD matching criterion. Also we showed that the second order matching prior matches alternative coverage probabilities up to the second order. It turns out that the one-at-a-time reference prior satisfies a second order matching criterion. Some simulation study is performed.

• Communications for Statistical Applications and Methods
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• 제15권3호
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• pp.429-440
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• 2008

In this paper, we develop the noninformative priors when the parameter of interest is the common coefficient of variation in two inverse Gaussian distributions. We want to develop the first and second order probability matching priors. But we prove that the second order probability matching prior does not exist. It turns out that the one-at-a-time and two group reference priors satisfy the first order matching criterion but Jeffreys' prior does not. The Bayesian credible intervals based on the one-at-a-time reference prior meet the frequentist target coverage probabilities much better than that of Jeffreys' prior. Some simulations are given.

• Journal of the Korean Data and Information Science Society
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• 제27권3호
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• pp.835-844
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• 2016

We develop the testing procedures about the homogeneity of the shape parameters of several inverse Gaussian distributions in our paper. We propose default Bayesian testing procedures for the shape parameters under the reference priors. The Bayes factor based on the proper priors gives the successful results for Bayesian hypothesis testing. For the case of the lack of information, the noninformative priors such as Jereys' prior or the reference prior can be used. Jereys' prior or the reference prior involves the undefined constants in the computation of the Bayes factors. Therefore under the reference priors, we develop the Bayesian testing procedures with the intrinsic Bayes factors and the fractional Bayes factor. Simulation study for the performance of the developed testing procedures is given, and an example for illustration is given.

• Advances in aircraft and spacecraft science
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• 제7권6호
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• pp.495-516
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• 2020

Nonlinear state estimation is a desirable and required technique for many situations in engineering (e.g., aircraft/spacecraft tracking, space situational awareness, collision warning, radar tracking, etc.). Due to high standards on performance in these applications, in the last few decades, there was an increasing demand for methods that are able to provide more accurate results. However, because of the mathematical complexity introduced by the nonlinearities of the models, the nonlinear state estimation uses techniques that, in practice, are not so well-established which, leads to sub-optimal results. It is important to take into account that each method will have advantages and limitations when facing specific environments. The main objective of this paper is to provide a comprehensive overview and interpretation of the most well-known methods for nonlinear state estimation with Gaussian priors. In particular, the Kalman filtering methods: EKF (Extended Kalman Filter), UKF (Unscented Kalman Filter), CKF (Cubature Kalman Filter) and EnKF (Ensemble Kalman Filter) with an aerospace perspective.

• Journal of the Korean Data and Information Science Society
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• 제26권3호
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• pp.739-748
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• 2015

This paper deals with the problem of testing about the equality of the scale parameters in several inverse Gaussian distributions. We propose default Bayesian testing procedures for the equality of the shape parameters under the reference priors. The reference prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. Therefore we propose the default Bayesian testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

• 응용통계연구
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• 제17권1호
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• pp.49-60
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• 2004

이 논문의 목적은 역 가우스 분포의 모수비가 관심의 대상일 때, 그 모수비에 대한 무정보적 사전분포를 구하는데 있다. 특별히, 모수비에 대한 확률대응사전분포와 기준 사전분포를 제안하였다. 먼저, 관심의 대상이 되는 모수에 대해 모수 직교화 변환을 구하고, 모수 직교화 변환을 이용하여 확률대응사전분포와 기준사전분포를 구하였다. 특히 확률대응사전분포의 일치차수는 1차임을 보였으며 2차 확률대응사전분포는 존재하지 않음을 보였다. 또한 제안된 사전분포에 의해 유도된 사후분포는 적절 분포임을 증명하였다. 모의 실험을 통하여 확률대응사전분포와 기준사전분포를 비교했으며, 실제자료를 이용하여 분석하는 예를 보였다.

• Journal of the Korean Data and Information Science Society
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• 제16권3호
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• pp.539-547
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• 2005

We propose the Bayesian testing for the equality of two independent Inverse Gaussian population means using the fractional Bayesian factors suggested by O' Hagan(1995). As prior distribution for the parameters, we assumed the noninformative priors. In order to investigate the usefulness of the proposed Bayesian testing procedures, the behaviors of the proposed results are examined via real data analysis.

• Journal of Radiation Protection and Research
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• 제41권2호
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• pp.149-154
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• 2016

Background: Any real application of Bayesian inference must acknowledge that both prior distribution and likelihood function have only been specified as more or less convenient approximations to whatever the analyzer's true belief might be. If the inferences from the Bayesian analysis are to be trusted, it is important to determine that they are robust to such variations of prior and likelihood as might also be consistent with the analyzer's stated beliefs. Materials and Methods: The robust Bayesian inference was applied to atmospheric dispersion assessment using Gaussian plume model. The scopes of contaminations were specified as the uncertainties of distribution type and parametric variability. The probabilistic distribution of model parameters was assumed to be contaminated as the symmetric unimodal and unimodal distributions. The distribution of the sector-averaged relative concentrations was then calculated by applying the contaminated priors to the model parameters. Results and Discussion: The sector-averaged concentrations for stability class were compared by applying the symmetric unimodal and unimodal priors, respectively, as the contaminated one based on the class of ${\varepsilon}$-contamination. Though ${\varepsilon}$ was assumed as 10%, the medians reflecting the symmetric unimodal priors were nearly approximated within 10% compared with ones reflecting the plausible ones. However, the medians reflecting the unimodal priors were approximated within 20% for a few downwind distances compared with ones reflecting the plausible ones. Conclusion: The robustness has been answered by estimating how the results of the Bayesian inferences are robust to reasonable variations of the plausible priors. From these robust inferences, it is reasonable to apply the symmetric unimodal priors for analyzing the robustness of the Bayesian inferences.

• Communications for Statistical Applications and Methods
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• 제19권6호
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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.