Discrete Support Set Selection for Gamma Prior Density Estimation in Measurement Error Model using Empirical Bayes Deconvolution
Keywords:
Bias, conjugate, hyperparameter, loglikelihood, PoissonAbstract
This paper discusses the empirical Bayes deconvolution (EBD) method in estimating gamma’s prior density for count data when the true or unobserved random variable is subject to measurement error. The observed random variable is related to the unobserved random variable by an additive measurement error model. The count data
are assumed to follow a Poisson distribution as realizations from an unknown prior density
Then the EBD method is applied to estimate
for every discretization point in the discrete support set of
The effect of selecting discrete support set for estimating gamma’s prior density based on the EBD method is illustrated by using simulation. It is shown that by selecting discretization set for Poisson data and gamma density as a prior distribution, the larger domain, and more points in discrete support set, the smaller value of bias, and standard deviation for gamma prior density estimate. Finally, assuming that the number of high school student dropout follows Poisson distribution, the EBD method is applied to estimate the prior probability distribution for high school student dropout data in 9 cities and 18 districts in West Java province.