Statistical Theory of Reliability.

In this paper, we develop noninformative priors for the log-normal distributionswhen the parameter of interest is the common mean. We developed Je reys’ prior, thereference priors and the rst order matching priors. It turns out that the reference priorsand Je reys’ prior do not satisfy a rst order matching criterion, and Je reys’ prior,the reference prior and the rst order matching prior are di erent. Some simulationstudy is performed and a real example is given.Keywords: Common mean, log-normal distribution, matching prior, reference prior. 1. Introduction The log-normal distribution is used in a wide range of applications, when the multiplica-tive scale is appropriate and the log-transformation removes the skew and brings aboutsymmetry of the data distribution (Limpert et al., 2001). Normality is the preferred dis-tributional assumption in many contexts, and logarithm is often the most commonly usedtransformation that an analyst considers to promote it. However, there are instances whenmoments, and the expectation in particular, are of interest on the original scale. For exam-ple, the log-normal distribution is frequently applied to variables in environmental science(Parkhurst, 1998), occupational health research (Rappaport and Selvin, 1987), health ex-penditure (Zhou et al., 1997), monetary units (Zabel, 1999; Longford and Pittau, 2006), etc.The population mean of such a variable may be a much more relevant target for inferencethan the population mean of its logarithm.The present paper focuses on developing noninformative priors for the common mean ofthe log-normal distributions. In the absence of sources of information or past data, Bayesianmethods rely on the objective priors or the noninformative priors.We consider Bayesian priors such that the resulting credible intervals for the commonlog-normal mean have coverage probabilities equivalent to their frequentist counterparts.Although this matching can be justi ed only asymptotically, our simulation results indicate

Noninformative priors for the common mean in Log-normal distributions

This article deals with the problem of testing for the correlation coecient in thebivariate normal distribution. We propose Bayesian hypothesis testing procedures forthe bivariate normal correlation coecient under the noninformative prior. The nonin-formative priors are usually improper which yields a calibration problem that makes theBayes factor to be de ned up to a multiplicative constant. So we propose the defaultBayesian hypothesis testing procedures based on the fractional Bayes factor and theintrinsic Bayes factors under the reference priors. A simulation study and an exampleare provided.Keywords: Bivariate normal distribution, correlation coecient, fractional Bayes factor,intrinsic Bayes factor, reference prior. 1. Introduction Let (X;Y) be a random vector distributed as a bivariate normal distribution BN( 1 ; 2 ;˙ 1 ;˙ 2 ;ˆ) with means  1 and  2 , variances ˙1 2 and ˙ 2 , and correlation coecient ˆ. Theprobability density function of (X;Y) is given byf(x;yj 1

Default Bayesian testing for the bivariate normal correlation coefficient

In this paper, we develop the reference priors for the common location parameter in the half-normal distributions with unequal scale paramters. We derive the reference priors as noninformative prior and prove the propriety of joint posterior distribution under the general prior including the reference priors. Through the simulation study, we show that the proposed reference priors match the target coverage probabilities in a frequentist sense.

Noninformative priors for the common location parameter in half-normal distributions

In this paper, we consider the hypothesis testing for the homogeneity of the shape parameters in the gamma distributions. The noninformative priors such as Jeffreys# prior or reference prior are usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the objective Bayesian testing procedure for the homogeneity of the shape parameters based on the fractional Bayes factor and the intrinsic Bayes factor under the reference prior. Simulation study and a real data example are provided.

Bayesian Hypothesis Testing for Homogeneity of the Shape Parameters in the Gamma Populations

This paper derives noninformative priors for scale parameter of exponential distribution when the data are collected in multiple step stress accelerated life tests. We nd the objective priors for this model and show that the reference prior satisfies first order matching criterion. Also, we show that there exists no second order matching prior. Some simulation results are given and using artificial data, we perform Bayesian analysis for proposed priors.

An objective Bayesian analysis for multiple step stress accelerated life tests

This article deals with the problem of testing mean when the coecient of variationin normal distribution is known. We propose Bayesian hypothesis testing procedures forthe normal mean under the noninformative prior. The noninformative prior is usuallyimproper which yields a calibration problem that makes the Bayes factor to be de nedup to a multiplicative constant. So we propose the objective Bayesian hypothesis testingprocedures based on the fractional Bayes factor and the intrinsic Bayes factor under thereference prior. Specially, we develop intrinsic priors which give asymptotically sameBayes factor with the intrinsic Bayes factor under the reference prior. Simulation studyand a real data example are provided.Keywords: Coecient of variation, fractional Bayes factor, intrinsic Bayes factor, in-trinsic prior, normal mean, reference prior. 1. Introduction Normal distribution has been widely used to model various phenomena in agricultural,biological, environmental and physical sciences. A problem of interest is the inference con-cerning normal mean when the coecient of variation is known. The assumption of a knowncoecient of variation is actually common in many clinical chemistry and pharmaceuticalsciences (Gleser and Healy, 1976).For example, when batches of some substance or chemicals are to be analyzed, if sucientbatches of the substances are analyzed, their coecient of variation will be known. In agri-cultural experiments, it is customary to conduct multi-locational trials. When the results ofa few centers are available, the coecient of variation is known and it can be used for theinferential purpose of an experiment to be conducted in a new location. In environmentalstudies, such situations arise when the standard deviation of a pollutant is directly related

Default Bayesian testing for normal mean with known coefficient of variation

In this paper, we develop the noninformative priors for the reliability in a stress-strength model where a strength X and a stress Y have independent exponential distributions with different scale parameters and a common location parameter. We derive the reference priors and prove the propriety of joint posterior distribution under the general prior including the reference priors. Through the simulation study, we show that the proposed reference priors match the target coverage probabilities in a frequentist sense.

Lee， WooDong

Papers

An objective Bayesian analysis for multiple step stress accelerated life tests

Default Bayesian testing for normal mean with known coefficient of variation

Reference priors for two parameter exponential stress-strength model

Objective Bayesian multiple hypothesis testing for the shape parameter of generalized exponential distribution