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Seminars

Prediction with Confidence – General Framework for Predictive Inference

  • 2019-12-18 (Wed.), 11:00 AM
  • R6005, Research Center for Environmental Changes Building
  • Prof. Regina Liu
  • Department of Statistics, Rutgers University

Abstract

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 for prescribing the notion of confidence under the frequentist interpretation and? providing meaningful answers for prediction-related questions. Its very form of a distribution function also lends itself as a useful tool for quantifying uncertainty in prediction. 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. 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 associated 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 even dependent data settings. ? This is joint work with Jieli Shen (Goldman Sachs) and Minge Xie (Rutgers University).

Update:2024-12-10 16:55
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