摘要：In this paper, we address the issue of estimation of the hierarchical Bayesian models, especially for count data in small area estimation problem. This model was developed by combining the existing terminology in generalized linear models with the concept of Bayes methods, especially hierarchical Bayes methods, such that it can be implemented to address the problem of small area estimation for survey data in the form of the count data. Development of this model starts by assuming that the observed random variable is a member of the exponential family conditional on a certain parameter. The main objective of the development of this model is to make inference on these parameters are also considered as random variables. Then these parameters are modeled with the Fay-Herriot model as the basic model of the small area estimation. Furthermore, the combination of both models will be standardized in such a way as to represent a model within the framework of Bayes methods that will eventually form a two-level hierarchical Bayes Poisson model to solve problems in small area estimation.
关键词：small area estimation;Fay-Herriot model;generalized linear models;Poisson distribution;Markov chain Monte Carlo;Gibbs sampling.
