Objective bayesian inference for quantile ratios in normal models

In medical research, it is important to compare quantiles of certain measures obtained from treatment and control groups, with the quantile ratio showing the effect of the treatment. In particular, inference of the quantile ratio based on large sample methods can be studied using a normal model. In this paper, we develop noninformative priors such as probability matching priors and reference priors for quantile ratios in normal models. It has been proved that the one-at-a-time reference prior satisfies a first-order matching criterion, while the Jeffreys' and two-group reference priors do not when the variances are equal. Through simulation study and an example based on real data, we also confirm that the proposed probability matching priors match the target coverage probabilities in a frequentist sense even when the sample size is small.