Prior-Free Probabilistic Prediction of Future Observations

Abstract

Prediction of future observations is a fundamental problem in statistics. Here we present a general approach based on the recently developed inferential model (IM) framework. We employ an IM-based technique to marginalize out the unknown parameters, yielding prior-free probabilistic prediction of future observables. Verifiable sufficient conditions are given for validity of our IM for prediction, and a variety of examples demonstrate the proposed method’s performance. Thanks to its generality and ease of implementation, we expect that our IM-based method for prediction will be a useful tool for practitioners. Supplementary materials for this article are available online.

• Disease count data
• Environmental data
• Inferential model
• Plausibility
• Prediction interval
• System breakdown data
• Validity

ACKNOWLEDGMENTS

The authors thank Chuanhai Liu for some fruitful discussions, Nicholas Karonis for cluster computer access, John Winans for computational assistance, and two anonymous reviewers for their helpful suggestions. This research is partially supported by the U.S. National Science Foundation, DMS-1208833.