Objective Bayesian analysis for masked data under symmetric assumption

In this paper, we consider an exponential model with masked data. We show that the parameters are nonidentifiable under a general masking probability assumption, and under symmetric assumption find a prior based on which the posterior means of parameters coincide with their MLEs. The Jeffreys prior and the reference prior are also derived under symmetric assumption. Propriety of the posteriors under the Jeffreys prior and the reference prior is assessed. When the hazard function of the series system is of interest, a reparametrization is considered, and we derive Jeffreys prior and the reference prior under the reparametrization. Then the frequentist coverage probabilities of the a- quantiles of the marginal posterior distributions of the parameters are obtained. The simulation study shows that the reference prior performs better than the Jeffreys prior in meeting the target coverage probabilities.