Highest Posterior Density Matching Research Articles

Objective priors for common correlation coefficient in bivariate normal populations

Various objective priors have been defined for the common correlation coefficient concerning several bivariate normal populations. In this paper, the proposed approach relies on the asymptotic matching of coverage probabilities corresponding to Bayesian credible intervals considering the corresponding frequentist ones. In the present paper, we focus on several matching criteria including quantile matching, distribution function matching, highest posterior density matching, and matching via inversion of test statistics. In addition, we consider reference priors for different groups of ordering. The proposed methods are investigated and compared between each other in terms of a frequentist coverage probability and then, they are illustrated through a simulation study and two real data examples.

Objective Bayesian inference for the ratio of the scale parameters of two Weibull distributions

ABSTRACTThe Weibull distribution is widely used due to its versatility and relative simplicity. In our paper, the non informative priors for the ratio of the scale parameters of two Weibull models are provided. The asymptotic matching of coverage probabilities of Bayesian credible intervals is considered, with the corresponding frequentist coverage probabilities. We developed the various priors for the ratio of two scale parameters using the following matching criteria: quantile matching, matching of distribution function, highest posterior density matching, and inversion of test statistics. One particular prior, which meets all the matching criteria, is found. Next, we derive the reference priors for groups of ordering. We see that all the reference priors satisfy a first-order matching criterion and that the one-at-a-time reference prior is a second-order matching prior. A simulation study is performed and an example given.

Noninformative priors for the ratio of the shape parameters of two Weibull distributions

The Weibull distribution is one of the most widely used lifetime distributions in reliability engineering. Here, the noninformative priors for the ratio of the shape parameters of two Weibull models are introduced. The first criterion used is the asymptotic matching of the coverage probabilities of Bayesian credible intervals with the corresponding frequentist coverage probabilities. We develop the probability matching priors for the ratio of the shape parameters using the following matching criteria: quantile matching, matching of the distribution function, highest posterior density matching, and matching via inversion of the test statistics. We obtain one particular prior that meets all the matching criteria. Next, we derive the reference priors for different groups of ordering. Our findings show that some of the reference priors satisfy a first-order matching criterion and the one-at-a-time reference prior is a second-order matching prior. Lastly, we perform a simulation study and provide a real-world example.

Noninformative priors for the common shape parameters of Weibull distributions

The Weibull distribution is widely used in survival analysis, reliability engineering, and failure analysis. In this paper, we develop noninformative priors such as probability matching priors for the common shape parameter of Weibull models using the asymptotic matching of coverage probabilities of Bayesian credible intervals with the corresponding frequentist coverage probabilities. Here, various matching criteria, such as quantile matching, matching of distribution function, highest posterior density matching, and matching via inversion of test statistics, are considered. Next, we derive the reference priors for groups of ordering. It also shows that most reference priors do not satisfy the first order matching criterion, but the one-at-a-time reference prior is the second order matching priors. A simulation study is performed and a real example is given.

Noninformative priors for the generalized half-normal distribution

In this paper, we develop noninformative priors for the generalized half-normal distribution when scale and shape parameters are of interest, respectively. Especially, we develop the first and second order matching priors for both parameters. For the shape parameter, we reveal that the second order matching prior is a highest posterior density (HPD) matching prior and a cumulative distribution function (CDF) matching prior. In addition, it matches the alternative coverage probabilities up to the second order. For the scale parameter, we reveal that the second order matching prior is neither a HPD matching prior nor a CDF matching prior. Also, it does not match the alternative coverage probabilities up to the second order. For both parameters, we present that the one-at-a-time reference prior is a second order matching prior. However, Jeffreys’ prior is neither a first nor a second order matching prior. Methods are illustrated with both a simulation study and a real data set.

Non-informative priors for the inverse Weibull distribution

In this paper, we develop the non-informative priors for the inverse Weibull model when the parameters of interest are the scale and the shape parameters. We develop the first-order and the second-order matching priors for both parameters. For the scale parameter, we reveal that the second-order matching prior is not a highest posterior density (HPD) matching prior, does not match the alternative coverage probabilities up to the second order and is not a cumulative distribution function (CDF) matching prior. Also for the shape parameter, we reveal that the second-order matching prior is an HPD matching prior and a CDF matching prior and also matches the alternative coverage probabilities up to the second order. For both parameters, we reveal that the one-at-a-time reference prior is the second-order matching prior, but Jeffreys’ prior is not the first-order and the second-order matching prior. A simulation study is performed to compare the target coverage probabilities and a real example is given.

Bayesian and likelihood-based inference for the bivariate normal correlation coefficient

The paper develops some objective priors for correlation coefficient of the bivariate normal distribution. The criterion used is the asymptotic matching of coverage probabilities of Bayesian credible intervals with the corresponding frequentist coverage probabilities. The paper uses various matching criteria, namely, quantile matching, highest posterior density matching, and matching via inversion of test statistics. Each matching criterion leads to a different prior for the parameter of interest. We evaluate their performance by comparing credible intervals through simulation studies. In addition, inference through several likelihood-based methods have been discussed.