COPSS Elizabeth L. Scott Lecture

Advanced data acquisition technology nowadays has often made inferences from diverse data sources easily accessible. Fusion learning refers to fusing inferences from multiple sources or studies to make more effective overall inference. We focus on the tasks: 1) Whether/When to combine inferences? 2) How to combine inferences efficiently? 3) How to combine inference to enhance the inference for a target study? We present a general framework for nonparametric and efficient fusion learning. The main tool underlying this framework is the new notion of depth confidence distribution (depth-CD), 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 approach is efficient, general and robust, and readily applies to heterogeneous studies with a broad range of complex settings. The approach is demonstrated with an aviation safety analysis application in tracking aircraft landing performance. This is joint work with Dungang Liu (U. Cincinnati) and Minge Xie (Rutgers University).