ABSTRACT
In Part III, we work with a single demographic array containing counts such as births or deaths, or totals such as health expenditure. We assume that the array has no measurement errors, though it may have some missing values. With most models, we also assume that we have an array measuring exposures or population sizes. The exposures array has no measurement errors and no missing values.
We treat the elements of the observed array as random draws from probability distributions. The probability distributions are governed by the elements in an array of super-population rates, probabilities, or means. The models of Part III generate estimates of the super-population rates, probabilities, or means, as well as parameters from the prior model for the super population rates, probabilities, or means.
The methods are useful for learning about demographic rates and propensities when sample sizes are too small for direct estimates to be reliable. By examining the smoothed rates, probabilities, or means, or the more abstract parameters in the prior model, we can gain insights into the demographic series that we would not gain by looking at direct estimates. The methods are also needed for dealing with missing data or forecasting.
