Normal-Compound Gamma priors with Count Data

Abstract

Count data models have become very common in several disciplines in recent years. Since these types of models can often be studied incorrectly using OLS methods, several solutions have been proposed to address this problem. One of these methods the normal-scale mixture method with different types of priors of the scale parameter. The importance of this method is to solve the issue of the bias-variance tradeoff by adding a local scale parameter to reduce the variance at the origin and reduce the bias at the tails. In this paper, a compound-gamma prior is placed for the scale parameter and the relevant Gibbs sampler is solved for posterior inference. The comparison of the performance of the proposed model with some other existing methods using both very sparse and low sparsity simulated data shows that the proposed model performs very well.