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. / Doctor of Philosophy / Typically, statisticians work with parametric distributions governing independent observations. However, sometimes operating under the assumption of independence severely limits us. We motivate the move away from independent sampling via the scope of Agent-based Modeling (ABM), where full populations are needed. The assumption of independence, when applied to synthesizing populations, leads to unwanted results; specifically, all synthetic populations generated from the sample sample data are essentially the same. As statisticians, this is clearly problematic because given only a small subset of the population, we clearly do not know what the population looks like, and thus any model which always gives the same answer is fundamentally flawed. We fix this problem by utilizing a new class of distributions which we call spacing priors, which allow us to create synthetic populations of individuals which are not independent of each other.

The presence of naturally occurring and man-made public health threats necessitate the design and implementation of mitigation strategies, such that adequate response is provided in a timely manner. Since multiple variables, such as geographic properties, resource constraints, and government mandated time-frames must be accounted for, computational methods provide the necessary tools to develop contingency response plans while respecting underlying data and assumptions. A typical response scenario involves the placement of points of dispensing (PODs) in the affected geographic region to supply vaccines or medications to the general public. Computational tools aid in the analysis of such response plans, as well as in the strategic placement of PODs, such that feasible response scenarios can be developed. Due to the sensitivity of bio-emergency response plans, geographic information, such as POD locations, must be kept confidential. The generation of synthetic geographic regions allows for the development of emergency response plans on non-sensitive data, as well as for the study of the effects of single geographic parameters. Further, synthetic representations of geographic regions allow for results to be published and evaluated by the scientific community. This dissertation presents methodology for the analysis of bio-emergency response plans, methods for plan optimization, as well as methodology for the generation of synthetic geographic regions.