Bayesian estimation of rare sensitive attribute

Randomized response models have been used to estimate a population proportion of a sensitive attribute. A randomized device is typically employed to protect respondent's privacy in a survey. In addition, an unrelated question is asked to improve the statistical efficiency. In this article, we propose Bayesian estimation of rare sensitive attribute using randomized response technique, which includes a rare unrelated attribute. Two cases are considered, the proportion of a rare unrelated attribute is known and unknown. A simulation study is conducted to assess the performance of the models using mean absolute error and coverage probability. The results show that the performance depends on the parameters and is robust to priors.