Objective priors for the ratio of scale parameters in generalized half normal distributions

.In this study, we conducted an objective Bayesian analysis focused on the ratio of scale parameters within generalized half-normal distributions. To support this analysis, we developed non informative priors, derived probability matching priors, and established reference priors. We successfully identified a second-order matching prior that satisfied all specified matching criteria. Our results demonstrated that Jeffreys’ prior and the two-group reference prior adhered to a first-order matching criterion, while the one-at-a-time reference prior was classified as a second-order matching prior. Additionally, we outlined the conditions required for the propriety of posterior distributions under general priors, including the non informative priors we formulated. To evaluate the effectiveness of the proposed priors, we performed a simulation study, which indicated that the one-at-a-time reference prior corresponds with target coverage probabilities from a frequentist standpoint. We further illustrated our methodology through real data examples.