UC Irvine

What is the right statistical theory for scientific practice? What are the distinctive dynamics of social learning and conformity? And what can disagreement between theoretical models teach us? This dissertation consists of essays that engage just these questions.

Chapter 1 examines explanations for a broadly maligned research practice, HARKing, which has been called one of the ‘four horsemen’ of the replication crisis in the social and biomedical sciences (alongside publication bias, low statistical power, and p-hacking). In it, I demonstrate how classical accounts of why HARKing undermines the reliability of scientific findings must be wrong, and proffer what I take to be the correct, Bayesian account for when and why HARKing is in fact bad. Further, I consider the implications of all this for a prominent proposal for methodological reform in the context of the replication crisis.

Chapter 2 consists of more exploratory work, produced in collaboration with my colleague Cole Williams. We propose a simple model of social learning on networks under the influence of conformity bias. In our model, heterogeneous agents express public opinions where those expressions are driven by the competing priorities of accuracy and of conformity to one’s peers. Agents learn, by Bayesian conditionalization, from private evidence from nature, and from the public declarations of other agents. Our key findings are that networks that produce configurations of social relation- ships that sustain a diversity of opinions empower honest communication and more accurate beliefs and that the networks that do this best turn out to be those which are both less centralized and less connected.

Finally, chapter 3 consists of elucidating the relationship between two key models in evolutionary game theory–the replicator dynamics and Moran process. These models are connected by a mean-field relation- ship—the former describes the expected behavior of the latter. However, there are conditions under which their predictions diverge. I demonstrate that the divergence between their predictions is a function of standard techniques used in their analysis, and of differences in the idealizations involved in each. My analysis reveals problems for stochastic stability analysis in a broad class of games. I demonstrate a novel domain of agreement between the dynamics and consider a simple moral for scientific modeling.