Computational Bayesian inference for estimating the size of a finite population

We develop computationally intensive Bayesian methods to estimate the size of a closed population and apply these methods to estimate the number of children born in upstate New York with spina bifida from 1969 to 1974. The names of these children may appear on three different administrative lists: medical; birth; and death records. We assume diffuse prior distributions on the marginal probabilities of a name appearing on each record and on the various odds ratios modeling the interactions of these lists. Samples from the posterior distribution are generated using a modified sample–resample technique. A Bayesian log-linear model is developed and the posterior distribution is sampled from a Markov chain generated using the Metropolis algorithm. These two approaches are compared in terms of their interpretability and computational complexity.