Inference for Populations:  Uncertainty Propagation via Bayesian Population Synthesis

In this dissertation, we develop a new type of prior distribution, specifically for populations themselves, which we denote the Dirichlet Spacing prior. This prior solves a specific problem that arises when attempting to create synthetic populations from a known subset: the unfortunate reality that assuming independence between population members means that every synthetic population will be essentially the same. This is a problem because any model which only yields one result (several very similar results), when we have very incomplete information, is fundamentally flawed. We motivate our need for this new class of priors using Agent-based Models, though this prior could be used in any situation requiring synthetic populations.