Graphical methods in prior elicitation.
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Casement, Christopher James, 1987-
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Prior elicitation is the process of quantifying an expert's belief in the form of a probability distribution on a parameter(s) to be used in a Bayesian data analysis. Existing methods require experts to quantify their belief by specifying multiple distribution summaries, which are then converted into the parameters of a given prior family. The resulting priors, however, may not accurately represent the expert's opinion, which in turn can undermine the accuracy of an analysis. In this dissertation we propose two interactive graphical strategies for prior elicitation, along with web-based Shiny implementations for each, that do not rely on an expert's ability to reliably quantify thier beliefs. Instead, the expert moves through a series of tests where they are tasked with selecting hypothetical future datasets they believe to be most likely from a collection of candidate datasets that are presented in graphical form. The algorithms then convert these selections into a prior distribution on the parameter(s) of interest. After discussing each elicitation method, we propose a variation on the Metropolis-Hastings algorithm that provides support for the underlying stochastic scheme in the second of the two elicitation strategies. We apply the methods to data models that are commonly employed in practice, such as Bernoulli, Poisson, and Normal, though the methods can be more generally applied to other univariate data models.