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.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/116057 |
| Date | 16 August 2023 |
| Creators | Grubb, Christopher Thomas |
| Contributors | Statistics, House, Leanna L., Datta, Jyotishka, Higdon, David, Van Mullekom, Jennifer H. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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