Prediction with Confidence – a General Framework for Predictive Inference
Regina Liu, Department of Statistics, Rutgers University, USA
We propose a general framework for prediction in which a prediction is in the form of a distribution function called “predictive distribution function.” This predictive distribution function is well suited to prescribing the notion of confidence under the frequentist interpretation, and it can provide meaningful answers for prediction-related questions. A general approach under this framework is formulated and illustrated using the so-called confidence distributions (CDs). This CD-based prediction approach inherits many desirable properties of CD, including its capacity to serve as a common platform for directly connecting the existing procedures of predictive inference in Bayesian, fiducial, and frequentist paradigms. We discuss the theory underlying the CD-based predictive distribution and related efficiency and optimality issues. We also propose a simple yet broadly applicable Monte-Carlo algorithm for implementing the proposed approach. This concrete algorithm together with the proposed definition and associate theoretical development provide a comprehensive statistical inference framework for prediction. Finally, the approach is demonstrated by simulation studies and a real project on predicting the volume of application submissions to a government agency. The latter shows the applicability of the proposed approach to dependent data settings. This is joint work with Jieli Shen, Minge Xie, and Goldman Sachs.