Data-dependent probability matching priors for likelihood ratio and adjusted likelihood ratio statistics

We consider likelihood ratio statistics based on the usual profile likelihood and the standard adjustments thereof proposed in the literature in the presence of nuisance parameters. The role of data-dependent priors in ensuring approximate frequentist validity of posterior credible regions based on the inversion of these statistics is investigated. Unlike what happens with data-free priors, it is seen that the resulting probability matching conditions readily admit solutions which entail approximate frequentist validity of the highest posterior density region as well.     

Bayesian analysis of life-testing problems involving the weibull distribution

Credible and highest posterior density intervals for the reliability function and parameters of a two-parameter Weibull process are obtained and the estimates compared with their corresponding classical counterparts.     

Estimation of multiple gamma scale-parameters: bayes estimation subject to uniform domination

Simultaneous estimation of p gamma scale-parameters is considered under squared-error loss. The problem of minimizing, subject to uniform risk domination, the Bayes risk (or more generally the posterior expected loss) against certain conjugate or mixtures of conjugate priors is considered. Rather surprisingly, it is shown that the minimization can be done conditionally, thus avoiding variational arguments. Relative savings loss (and a posterior version thereof) are found, and it is found that in the most favorable situations, Bayesian robustness can be achieved without sacrificing substantial subjective Bayesian gains.     

Polya后验方法在有限总体抽样估计中的模拟研究

polya后验方法作为一种无信息贝叶斯估计方法,在有限总体抽样中,通过观测的样本,构造一系列的模拟总体,然后进行统计推断。通过统计模拟研究了polya后验方法估计的一些特点,并和Bootstrap方法进行比较。模拟结果显示:polya后验方法能够很好地估计总体的均值,随着样本量的增大,估计值与真值的差距越来越小。采用polya后验方法构造的置信区间区间长度较小,能够很好地覆盖真值。     

A bayesian analysis of the intraclass correlations in the mixed linear model

This article is concerned with the study of intraclass correlations in the mixed linear model. A brief account of the shortcomings of the existing meth¬ods (frequentist. likelihood and Bayesian) is followed by alternative Bayesian parametrizations involving intraclass correlations and variance ratios. Our prior specifications accommodate a priori dependencies as well as situations which involve little or no prior information. We give examples of interval estimation and hypothesis testing using data from an animal breeding study.     

Small sample set estimation of a baseline ranking

Ranking objects by a panel of judges is commonly used in situations where objective attributes cannot easily be measured or interpreted. Under the assumption that the judge independently arrive at their rankings by making pair wise comparisons among the objects in an attempt to reproduce a common baseline ranking w₀, we develop and explore confidence regions and Bayesian highest posterior density credible regions for w₀ with emphasis on very small sample sizes.     

A Bayesian Approach to the Estimation of Expected Cell Counts by Using Log-Linear Models

ABSTRACT

In this article, Bayesian estimation of the expected cell counts for log-linear models is considered. The prior specified for log-linear parameters is used to determine a prior for expected cell counts, by means of the family and parameters of prior distributions. This approach is more cost-effective than working directly with cell counts because converting prior information into a prior distribution on the log-linear parameters is easier than that of on the expected cell counts. While proceeding from the prior on log-linear parameters to the prior of the expected cell counts, we faced with a singularity problem of variance matrix of the prior distribution, and added a new precision parameter to solve the problem. A numerical example is also given to illustrate the usage of the new parameter.     

Bayesian estimation of sensitivity level and population proportion of a sensitive characteristic in a binary optional unrelated question RRT model

Sihm et al. (2016 Sihm, J. S., A. Chhabra, and S. N. Gupta. 2016. An optional unrelated question RRT model. Involve: A Journal of Mathematics 9 (2):195–209.[Crossref] , [Google Scholar]) proposed an unrelated question binary optional randomized response technique (RRT) model for estimating the proportion of population that possess a sensitive characteristic and the sensitivity level of the question. In our work, decision theoretic approach has been followed to obtain Bayes estimates of the two parameters along with their corresponding minimal Bayes posterior expected losses (BPEL) using beta prior and squared error loss function (SELF). Relative losses are also examined to compare the performances of the Bayes estimates with those of the classical estimates obtained by Sihm et al. (2016 Sihm, J. S., A. Chhabra, and S. N. Gupta. 2016. An optional unrelated question RRT model. Involve: A Journal of Mathematics 9 (2):195–209.[Crossref] , [Google Scholar]). The results obtained are illustrated with the help of real survey data using non informative prior.