An objective Bayesian analysis of dichotomous sensitive data

We consider a dichotomous population in which every person belongs either to a sensitive group $A$ or to the non sensitive complement $\bar{A}$. The object of interest is to estimate the population proportion of individuals who are members of $A$. We refer to a randomized response model proposed by Huang (2004), where also another parameter is present, namely the probability that a respondent truthfully states that he/she belongs to $A$ in a direct response survey. In the paper the posterior distribution of the parameters under the joint Jeffreys and Reference prior is derived. The properties of the noninformative priors are investigated through the frequentist coverage probabilities of posterior quantiles.