Bayesian estimation of a proportion under an asymmetric observation error
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Keywords
Bayesian estimation, Binomial distribution, Probability of false response, psychoactive drugs.
Abstract
The process of estimating a proportion that is associated with a sensitive question can yield responses that are not necessarily according to the reality.
To reduce the probability o false response to this kind of sensitive questions some authors have proposed techniques of randomized response assuming a
symmetric observation error. In this paper we present a generalization of the case where a symmetric error is assumed since this assumption could be unrealistic in practice. Under the assumption of an assymetric error the likelihood function is built. By doing this we intend that in practice the final user has
an alternative method to reduce the probability of false response. Assuming informative a priori distributions an expresion for the posterior distribution is found. Since this posterior distribution does not have a closed mathematical expression, it is neccesary to use the Gibbs sampler to carry out the estimation process. This technique is illustrated using real data about drug consumptions that were collected by the Oficina de Bienestar from the Universidad Nacional de Colombia at Medellín.
MSC: 62., 62-07, 62c12
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References
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