Bayesian estimation of sensitivity level and population proportion of a sensitive characteristic in a binary optional unrelated question RRT model

TLDR: In this article, decision theoretic approach has been followed to obtain Bayes estimates of the two parameters along with their corresponding minimal Bayes posterior expected losses (BPEL) using beta prior and squared error loss function (SELF).

Abstract: Sihm et al. (2016) proposed an unrelated question binary optional randomized response technique (RRT) model for estimating the proportion of population that possess a sensitive characteristic and the sensitivity level of the question. In our work, decision theoretic approach has been followed to obtain Bayes estimates of the two parameters along with their corresponding minimal Bayes posterior expected losses (BPEL) using beta prior and squared error loss function (SELF). Relative losses are also examined to compare the performances of the Bayes estimates with those of the classical estimates obtained by Sihm et al. (2016). The results obtained are illustrated with the help of real survey data using non informative prior.