A Note on Bayesian Estimation for the Negative-Binomial Model

2000 Mathematics Subject Classification: 62F15.

The Negative Binomial model, which is generated by a simple mixture model, has been widely applied in the social, health and economic market prediction. The most commonly used methods were the maximum likelihood estimate (MLE) and the moment method estimate (MME). Bradlow et al. (2002) proposed a Bayesian inference with beta-prime and Pearson Type VI as priors for the negative binomial distribution. It is due to the complicated posterior densities of interest not amenable to closed-form integration. A polynomial type expansion for the gamma function had been used to derive approximations for posterior densities by Bradlow et al. (2002). In this note, different parameters of interest are used to re-parameterize the model. Beta and gamma priors are introduced for the parameters and a sampling procedure is proposed to evaluate the Bayes estimates of the parameters. Through the computer simulation, the Bayesian estimates for the parameters of interest are studied via mean squared error and variance. Finally, the proposed Bayesian estimate is applied to model two real data sets.