Bayesian model selection is a useful tool for identifying an appropriate model class, dependence structure, and valuable predictors for a wide variety of applications. In this work we consider objective Bayesian model selection where no subjective information is available to inform priors on model parameters a priori, specifically in the case of hierarchical models for spatial data, which can have complex dependence structures. We develop an approach using trained priors via fractional Bayes factors where standard Bayesian model selection methods fail to produce valid probabilities under improper reference priors. This enables researchers to concurrently determine whether spatial dependence between observations is apparent and identify important predictors for modeling the response. In addition to model selection with objective priors on model parameters, we also consider the case where the priors on the model space are used to penalize individual predictors a priori based on their costs. We propose a flexible approach that introduces a tuning parameter to cost-penalizing model priors that allows researchers to control the level of cost penalization to meet budget constraints and accommodate increasing sample sizes. / Doctor of Philosophy / Spatial data, such as data collected over a geographic region, is relevant in many fields. Spatial data can require complex models to study, but use of these models can impose unnecessary computations and increased difficulty for interpretation when spatial dependence is weak or not present. We develop a method to simultaneously determine whether a spatial model is necessary to understand the data and choose important variables associated with the outcome of interest. Within a class of simpler, linear models, we propose a technique to identify important variables associated with an outcome when there exists a budget or general desire to minimize the cost of collecting the variables.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/115642 |
| Date | 03 July 2023 |
| Creators | Porter, Erica May |
| Contributors | Statistics, Franck, Christopher T., Ferreira, Marco A. R., Adams, Stephen Conway, House, Leanna L. |
| 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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