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<p>The Prediction of future observations with constraints is a fundamental problem in applied statistics. In this paper, we consider incorporating parameter constraints into the frequentist, Bayesian, fiducial and inferential model (IM) prediction frameworks. As two simple examples, the constrained Gaussian and Poisson models often appear in high energy physics and we use these two models to introduce constrained prediction methods. Since the prediction interval (PI) is a useful tool for predicting future data, our simulation studies show that the PIs of fiducial and IM have better coverage performance than the frequentist and Bayesian PIs. We also discuss the use of the fiducial and IM PIs. Finally, two real examples are used to demonstrate the application of different methods.</p>

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Prediction Intervals of Future Observations with Parameter Constraints

  • 期刊论文

  • 发表日期：

    2026年4月3日

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  • Hezhi Lu,
  • Hua Jin,
  • Zhining Wang,
  • Yuan Li

摘要

The Prediction of future observations with constraints is a fundamental problem in applied statistics. In this paper, we consider incorporating parameter constraints into the frequentist, Bayesian, fiducial and inferential model (IM) prediction frameworks. As two simple examples, the constrained Gaussian and Poisson models often appear in high energy physics and we use these two models to introduce constrained prediction methods. Since the prediction interval (PI) is a useful tool for predicting future data, our simulation studies show that the PIs of fiducial and IM have better coverage performance than the frequentist and Bayesian PIs. We also discuss the use of the fiducial and IM PIs. Finally, two real examples are used to demonstrate the application of different methods.