  We propose a novel Bayesian framework for the joint modeling of survey point
and variance estimates for count data. The approach incorporates an induced
prior distribution on the modeled true variance that sets it equal to the
generating variance of the point estimate, a key property more readily achieved
for continuous data response type models. Our count data model formulation
allows the input of domains at multiple resolutions (e.g., states, regions,
nation) and simultaneously benchmarks modeled estimates at higher resolutions
(e.g., states) to those at lower resolutions (e.g., regions) in a fashion that
borrows more strength to sharpen our domain estimates at higher resolutions. We
conduct a simulation study that generates a population of units within domains
to produce ground truth statistics to compare to direct and modeled estimates
performed on samples taken from the population where we show improved
reductions in error across domains. The model is applied to the job openings
variable and other data items published in the Job Openings and Labor Turnover
Survey administered by the U.S. Bureau of Labor Statistics.
