This paper suggests the nested error regression model, with use of uncertain random effects, which means that the random effects in each area are expressed as a mixture of a normal distribution and a positive mass at 0. For estimation of model parameters and prediction of random effects, we consider Bayesian yet objective inference by setting improper prior distributions on the model parameters. We show under the mild sufficient condition that the posterior distribution is proper and the posterior variances are finite to confirm validity of posterior inference. To generate samples from the posterior distribution, we provide the Gibbs sampling method. The full conditional distributions of the posterior distribution are all familiar forms such that the proposed methodology is easy to implement. This paper also addresses the problem of prediction of finite population means and we provide a sampling based method to tackle this issue. We compare the proposed model with the conventional nested error regression model through simulation and empirical studies. … Nested Error Regression Model google