| Abstract: | Bayes factors are increasingly used to provide evidence for hypothesis in statistical tests due to their ease of interpretation and ability to reflect evidence in favor of true null hypotheses. However, this dissertation shows that current definitions of Bayes factors used for tests in linear models often have severe computational issues for large sample sizes and poor convergence rates for true null hypothesis. Inconsistent results under a true null hypothesis mean that current methods are, in practice, not much different from their frequentist counterparts. To provide a better alternative to both frequentist tests and current Bayesian methods, we describe Bayes factors based on non-local alternative priors (NAPs) that have a closed form and are consistent for both true null and true alternative hypotheses. In simulation results and real data, we show that the NAP-based Bayes factors perform well under both true alternative and true null hypotheses and allow researchers to tailor their hypothesis testing to be more or less sensitive to different effect sizes. This dissertation shows Bayes factors using a specific NAP prior developed by Johnson and Rossell (2010) and based on the traditional model setup for Analysis of Variance (ANOVA) testing used by common Bayesian linear regression hypotheses testing models. Additionally, we show the moment generating function and subsequent moments of the NAP prior both exist and have a closed form. The electronic version of this dissertation is accessible from https://hdl.handle.net/1969.1/198494 |
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