• Title, Summary, Keyword: HPD interval

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On Estimation of HPD Interval for the Generalized Variance Using a Weighted Monte Carlo Method

  • Kim, Hea-Jung
    • Communications for Statistical Applications and Methods
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    • v.9 no.2
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    • pp.305-313
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    • 2002
  • Regarding to inference about a scalar measure of internal scatter of Ρ-variate normal population, this paper considers an interval estimation of the generalized variance, │$\Sigma$│. Due to complicate sampling distribution, fully parametric frequentist approach for the interval estimation is not available and thus Bayesian method is pursued to calculate the highest probability density (HPD) interval for the generalized variance. It is seen that the marginal posterior distribution of the generalized variance is intractable, and hence a weighted Monte Carlo method, a variant of Chen and Shao (1999) method, is developed to calculate the HPD interval of the generalized variance. Necessary theories involved in the method and computation are provided. Finally, a simulation study is given to illustrate and examine the proposed method.

A Bayesian Comparison of Two Multivariate Normal Genralized Variances

  • Kim, Hea-Jung
    • Proceedings of the Korean Statistical Society Conference
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    • pp.73-78
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    • 2002
  • In this paper we develop a method for constructing a Bayesian HPD (highest probability density) interval of a ratio of two multivariate normal generalized variances. The method gives a way of comparing two multivariate populations in terms of their dispersion or spread, because the generalized variance is a scalar measure of the overall multivariate scatter. Fully parametric frequentist approaches for the interval is intractable and thus a Bayesian HPD(highest probability densith) interval is pursued using a variant of weighted Monte Carlo (WMC) sampling based approach introduced by Chen and Shao(1999). Necessary theory involved in the method and computation is provided.

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On the Efficient Teaching Method of Confidence Interval in College Education

  • Kim, Yeung-Hoon;Ko, Jeong-Hwan
    • Journal of the Korean Data and Information Science Society
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    • v.19 no.4
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    • pp.1281-1288
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    • 2008
  • The purpose of this study is to consider the efficient methods for introducing the confidence interval. We explain various concepts and approaches about the confidence interval estimation. Computing methods for calculating the efficient confidence interval are suggested.

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Noninformative Priors for the Ratio of the Failure Rates in Exponential Model

  • Cho, Jang-Sik;Baek, Sung-Uk
    • Journal of the Korean Data and Information Science Society
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    • v.13 no.2
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    • pp.217-226
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    • 2002
  • In this paper, we derive noninformative priors for the ratio of failure rates in exponential model. A class of priors is found by matching the coverage probabilities of one-sided Baysian credible interval with the corresponding frequentist coverage probabilities. And we prove that the noninformative prior matches the alternative coverage probabilities and is a HPD matching prior up to the second order. Finally, we provide simulated freqentist coverage probabilities under the derived noninformative prior for small samples.

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Bayesian Model Selection in the Unbalanced Random Effect Model

  • Kim, Dal-Ho;Kang, Sang-Gil;Lee, Woo-Dong
    • Journal of the Korean Data and Information Science Society
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    • v.15 no.4
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    • pp.743-752
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    • 2004
  • In this paper, we develop the Bayesian model selection procedure using the reference prior for comparing two nested model such as the independent and intraclass models using the distance or divergence between the two as the basis of comparison. A suitable criterion for this is the power divergence measure as introduced by Cressie and Read(1984). Such a measure includes the Kullback -Liebler divergence measures and the Hellinger divergence measure as special cases. For this problem, the power divergence measure turns out to be a function solely of $\rho$, the intraclass correlation coefficient. Also, this function is convex, and the minimum is attained at $\rho=0$. We use reference prior for $\rho$. Due to the duality between hypothesis tests and set estimation, the hypothesis testing problem can also be solved by solving a corresponding set estimation problem. The present paper develops Bayesian method based on the Kullback-Liebler and Hellinger divergence measures, rejecting $H_0:\rho=0$ when the specified divergence measure exceeds some number d. This number d is so chosen that the resulting credible interval for the divergence measure has specified coverage probability $1-{\alpha}$. The length of such an interval is compared with the equal two-tailed credible interval and the HPD credible interval for $\rho$ with the same coverage probability which can also be inverted into acceptance regions of $H_0:\rho=0$. Example is considered where the HPD interval based on the one-at- a-time reference prior turns out to be the shortest credible interval having the same coverage probability.

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Classical and Bayesian studies for a new lifetime model in presence of type-II censoring

  • Goyal, Teena;Rai, Piyush K;Maury, Sandeep K
    • Communications for Statistical Applications and Methods
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    • v.26 no.4
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    • pp.385-410
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    • 2019
  • This paper proposes a new class of distribution using the concept of exponentiated of distribution function that provides a more flexible model to the baseline model. It also proposes a new lifetime distribution with different types of hazard rates such as decreasing, increasing and bathtub. After studying some basic statistical properties and parameter estimation procedure in case of complete sample observation, we have studied point and interval estimation procedures in presence of type-II censored samples under a classical as well as Bayesian paradigm. In the Bayesian paradigm, we considered a Gibbs sampler under Metropolis-Hasting for estimation under two different loss functions. After simulation studies, three different real datasets having various nature are considered for showing the suitability of the proposed model.

On Estimating Burr Type XII Parameter Based on General Type II Progressive Censoring

  • Kim Chan-Soo
    • Communications for Statistical Applications and Methods
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    • v.13 no.1
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    • pp.89-99
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    • 2006
  • This article deals with the problem of estimating parameters of Burr Type XII distribution, on the basis of a general progressive Type II censored sample using Bayesian viewpoints. The maximum likelihood estimator does not admit closed form but explicit sharp lower and upper bounds are provided. Assuming squared error loss and linex loss functions, Bayes estimators of the parameter k, the reliability function, and the failure rate function are obtained in closed form. Finally, a simulation study is also included.

Bayesian analysis of an exponentiated half-logistic distribution under progressively type-II censoring

  • Kang, Suk Bok;Seo, Jung In;Kim, Yongku
    • Journal of the Korean Data and Information Science Society
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    • v.24 no.6
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    • pp.1455-1464
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    • 2013
  • This paper develops maximum likelihood estimators (MLEs) of unknown parameters in an exponentiated half-logistic distribution based on a progressively type-II censored sample. We obtain approximate confidence intervals for the MLEs by using asymptotic variance and covariance matrices. Using importance sampling, we obtain Bayes estimators and corresponding credible intervals with the highest posterior density and Bayes predictive intervals for unknown parameters based on progressively type-II censored data from an exponentiated half logistic distribution. For illustration purposes, we examine the validity of the proposed estimation method by using real and simulated data.

A Bayesian Meta Analysis for Assessing Bioequivalence among Two Generic Copies of the Same Brand-Name Drug

  • Oh, Hyun-Sook
    • Communications for Statistical Applications and Methods
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    • v.13 no.2
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    • pp.285-295
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    • 2006
  • As more generic drugs become available, the quality, safety, and efficacy of generic drugs have become a public concern. Specifically, drug interchangeability among generic copies of the same brand-name drug is a safety concern. This research proposes a Bayesian method for assessing bioequivalence between two generic copies of the same brand-name drug from two independent $2{\times}2$ crossover design experiments. Uninformative priors are considered for general use and the posterior distribution of the difference of two generic drug effects is derived from which the highest probability density interval can be evaluated. Examples are presented for illustration.

Estimation of Geometric Mean for k Exponential Parameters Using a Probability Matching Prior

  • Kim, Hea-Jung;Kim, Dae Hwang
    • Communications for Statistical Applications and Methods
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    • v.10 no.1
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    • pp.1-9
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    • 2003
  • In this article, we consider a Bayesian estimation method for the geometric mean of $textsc{k}$ exponential parameters, Using the Tibshirani's orthogonal parameterization, we suggest an invariant prior distribution of the $textsc{k}$ parameters. It is seen that the prior, probability matching prior, is better than the uniform prior in the sense of correct frequentist coverage probability of the posterior quantile. Then a weighted Monte Carlo method is developed to approximate the posterior distribution of the mean. The method is easily implemented and provides posterior mean and HPD(Highest Posterior Density) interval for the geometric mean. A simulation study is given to illustrates the efficiency of the method.