Efficient Choice of Priors for Bayesian Hypothesis Tests in Psychology and for Dynamic Modeling of Zero-Inflated Directed Networks

Abstract

We propose efficient priors for two different statistical problems: (1) designing Bayesian hypothesis tests with reduced costs for detecting the presence or absence of hypothesized effects, and (2) efficient modeling of dynamic zero-inflated directed networks. Our contributions cover computational and methodological aspects and touch upon theoretical aspects in some cases.

Costs of conducting experiments to test hypothesized effects are often directly related to the number of tested items or participants. To address this, in the first part of the thesis we propose cost-efficient Bayesian hypothesis tests. We describe a modified sequential probability ratio test that can be used to reduce the average sample size required to perform statistical hypothesis tests at specified levels of significance and power. Examples are provided for z and t tests, and tests of binomial success probabilities. A description of the software package to implement the test is provided. We compare the sample sizes required in fixed design tests conducted at 5% significance levels to the average sample sizes required in sequential tests conducted at 0.5% significance levels, and we find that the two sample sizes are approximately equal. To generalize this framework, we found the default implementations of Bayesian tests prevent the accumulation of strong evidence in favor of true null hypotheses because associated default alternative hypotheses assign a high probability to data that are most consistent with a null effect. We propose the use of “non-local” alternative hypotheses to resolve this paradox. The resulting class of Bayesian hypothesis tests permits a more rapid accumulation of evidence in favor of both true null hypotheses and alternative hypotheses that are compatible with standardized effect sizes of most interest in psychology.

The second part of the thesis extends the discussion of choosing efficient priors and proposes the Hurdle Network Model for modeling zero-inflated directed networks. We assume node-specific dynamic latent attributes to account for the underlying network structure and apriori assume the Dynamic Shrinkage Process on them. We find the model has good predictive performance. Simulation studies and an application on bilateral trade flows from the apparel industry are included to support this.