Hierarchical Bayesian modeling with skew normal distribution

초록

In fact, most statistical surveys consist of sample surveys, not total surveys. This paper considers the Bayesian hierarchical modeling for estimation in surveys with non-sample. In our study, there are two different surveys and the variables of interest consist of skewed values. For this problem, we first use a matching algorithm for two surveys and then develop a Bayesian hierarchical model with skew normal distribution and noninformative priors. Bayesian hierarchical models have been widely used for small area estimation. The Bayesian hierarchical model is based on a very simple model, and can be set up using a very complex data model. The paper by Molina, Nandram, and Rao (2014) introduces a Bayesian hierarchical model of continuous, right-skewed data. In this study, skewed variables were estimated using log transformation, and our purpose is to develop the previous method using skew normal distribution for model assumptions. Skew normal distribution, a family of distributions including the standard normal but with an extra parameter to regulate skewness was first introduced by O'Hagan and Leonard(1976). Our model was evaluated by comparing with Nandram's model in simulation study.

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