Bayes estimation of ratio of scale-like parameters for inverse Gaussian distributions and applications to classification

We consider two inverse Gaussian populations with a common mean but different scale-like parameters, where all parameters are unknown. We construct noninformative priors for the ratio of the scale-like parameters to derive matching priors of different orders. Reference priors are proposed for different groups of parameters. The Bayes estimators of the common mean and ratio of the scale-like parameters are also derived. We propose confidence intervals of the conditional error rate in classifying an observation into inverse Gaussian distributions. A generalized variable-based confidence interval and the highest posterior density credible intervals for the error rate are computed. We estimate parameters of the mixture of these inverse Gaussian distributions and obtain estimates of the expected probability of correct classification. An intensive simulation study has been carried out to compare the estimators and expected probability of correct classification. Real data-based examples are given to show the practicality and effectiveness of the estimators.