Neyman Award & Lecture

Modern data acquisition technology has greatly increased the accessibility of complex inferences, based on summary statistics or sample data, from diverse data sources. Fusion learning refers to combining complex inferences from multiple sources or studies to make a more effective overall inference for the target parameters. We focus on the tasks: 1) Whether/When to combine inferences? 2) How to combine inferences efficiently? 3) How to combine inferences to enhance an individual study, thus named i-Fusion?

We present a general framework for nonparametric and efficient fusion learning for inference on multi-parameters, which may be correlated. The main tool underlying this framework is the new notion of depth confidence distribution (depth-CD), which is developed by combining data depth, bootstrap and confidence distributions. We show that a depth-CD is an omnibus form of confidence regions, whose contours of level sets shrink toward the true parameter value, and thus an all-encompassing inferential tool. The fusion approach is shown to be efficient, general and robust. It readily applies to heterogeneous studies with a broad range of complex and irregular settings. This property also enables the approach to utilize indirect evidence from incomplete studies to gain the hidden efficiency for the overall inference. The approach is demonstrated with simulation studies and real applications in tracking aircraft landing performance and in zero-event studies in clinical trials with non-estimable parameters.