Abstract—In this paper, we relax the fully parametric distributional assumption of measurement errors (MEs) to establish mixture Bernoulli model by a centered Dirichlet process. A hybrid algorithm is presented to generate observations required for a Bayesian inference from the posterior distributions of parameters and covariates subject to MEs in Bernoulli model by combining the stick-breaking prior and the Gibbs sampler together with the Metropolis-Hastings algorithm. Two Monte Carlo studies illustrate the superiority of the measurement error estimators in certain situations.

Index Terms—Monte Carlo, Bayesian estimation, Bernoulli model, measurement error.

Dewang Li, Meilan Qiu are with School of Mathematics and Big Data, Huizhou University, Huizhou, Guangdong, 516007, China (email: qml_1981@126.com).
Yuanying Zhao is with College of Mathematics and Information science, Guiyang University, Guizhou, 550005, China (zhaoyuanying_@126.com).

Cite: Dewang Li, Meilan Qiu, Yuanying Zhao, "Semiparametric Bayesian Estimation of Bernoulli Model with Measurement Error," International Journal of Applied Physics and Mathematics vol. 9, no. 4, pp. 167-172, 2019.