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In this paper, we examine the problem of estimating the sensitive char-acteristics and behaviors in a multinomial randomized response model usingBayesian approach. We derived a posterior distribution for parameter ofinterest for multinomial randomized response model. Based on the poste-rior distribution, we also calculated a credible intervals and mean squarederror (MSE). We nally compare the maximum likelihood estimator and theBayes estimator in terms of MSE.