Bayesian analysis of count data and its application in demography

Count-data modeling is often used in statistical applications, including demography. For example, annual counts of births and population in each county provide us valuable information in estimating age-specific fertility rate (ASFR) and fertility pattern which are two important subjects to demography researchers and policymakers. However, common issues encountered in modeling and estimating the count data are excessive zeros than expected by the standard Poisson model and large variabilities in parameter estimates caused by small sample sizes. Failure to take zero inflation and small sample size into account will cause large bias and variance in estimation.

In this dissertation, we propose a zero-inflated Poisson model with scaled-skew normal function (ZIP-SSN) as the trajectory of Poisson rates to estimate fertility pattern while accommodating excessive zeros in count data. To tackle the complexity of posterior sampling in parameter estimation, Markov chain Monte Carlo (MCMC) algorithms including the Metropolis-Hastings and the Gibbs sampling are implemented to sample the posterior distributions of parameters and construct associated Bayesian credible regions. Meanwhile, to estimate the ASFR for an individual county, we extend the Bayes hierarchical technique to the Bayes benchmarking approach in the sense that the aggregated estimator matches with the direct estimator of a larger geographical region. Such overall agreement with the larger region is important when the modeler needs to convince policy makers of the utility of the model.

A study on the fertility rate of 254 counties in Texas is carried out to demonstrate the utility of ZIP-SSN model in estimating ASFR pattern at larger geographical territory. The same data set is also used to demonstrate the superiority of Bayes benchmarking approach in total fertility rate estimation for an individual county of Texas.