Statistical Inference and Learning in Complex Experimental Settings

Abstract

This thesis presents three self-contained chapters: a powerful approach to partial conjunction hypothesis testing, an online reinforcement learning algorithm for scarce resource allocation in public health settings, and an experimental design for anytime valid inference on adaptive experiments. In Chapter 1, we propose a new method for partial conjunction hypothesis (PCH) testing, called the Conditional Partial Conjunction Hypothesis (cPCH) test. PCH tests are necessary to address important statistical questions in a diverse array of fields, from the analysis of causal graphs to the evaluation of scientific replicability. The cPCH test is less conservative, and hence, more powerful than existing approaches, and achieves particular power gains in low-signal regimes commonly encountered in applications such as genetic analysis. In Chapter 2, we propose a new experimental design for adaptive experiments that enables continuous inference on the Average Treatment Effect (ATE), with guarantees on statistical validity and power. In contrast to existing work, our approach does not require the treatment assignment probabilities of the adaptive assignment algorithm to be bounded away from zero and one, making it applicable to nearly any adaptive experimental design, including many common multi-armed bandit algorithms like Thompson sampling and the Upper Confidence Bound method. We empirically show that our design improves the power of ATE inference while maintaining valid finite-sample coverage across a wide array of experimental settings while paying relatively little cost in reward. In Chapter 3, we present a new online reinforcement learning algorithm for allocating scarce interventions in health program. By utilizing hierarchical Bayesian modeling approaches, our algorithm shares information within and across the program participants to learn the underlying transition dynamics quickly, even the algorithm only has a limited time horizon to interact with the system. Through an extensive simulation study, including one setting developed from real data from a mobile health service program in India, we showcase our algorithm’s ability to significantly improve retention in health program settings.