Implementasi Model Poisson Bayes Berhirarki Dua-Level untuk Memodelkan Data Cacahan pada Masalah Pendugaan Area Kecil

Abstract

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.