Inferences derived from various data sources can be combined, a process known as fusion learning, to produce more robust and powerful results compared to analyzing each data source individually. This research introduces a novel fusion learning approach called iFusion, which aims to generate effective personalized inferences by integrating statistical results from relevant data sources. By intelligently leveraging the knowledge of relevant individuals, iFusion improves the efficiency of individualized inference, exhibiting an oracle-like property under appropriate conditions. Moreover, iFusion demonstrates versatility and resilience in handling the inherent heterogeneity present in diverse data sources. These advancements make iFusion particularly well-suited for goal-oriented applications.
Main paper: Jieli Shen, Regina Y. Liu and Minge Xie. (2020) iFusion: Individualized fusion learning. Journal of the American Statistical Association 115:531, pages 1251-1267.
This research introduces a general framework for prediction that utilizes a predictive distribution function formulated by confidence distributions (CDs). By adopting this CD-based prediction approach, the framework inherits numerous desirable properties of CDs, making it a common platform for connecting and unifying existing procedures of predictive inference across Bayesian, fiducial, and frequentist paradigms. The theory underpinning the CD-based predictive distribution is thoroughly developed, addressing various efficiency and optimality considerations. Additionally, a simple yet broadly applicable Monte Carlo algorithm is proposed to facilitate the implementation of this approach in a wide range of applications.
Main paper: Jieli Shen, Regina Y. Liu and Minge Xie. (2020) Prediction with confidence - a general framework for predictive inference. Journal of Statistical Planning and Inference 195, pages 126-140.