Abstract

Frequentist and Bayesian approaches for interval estimation usually produce conflicting results if applied to analyze the same data set. Paradoxically, there is no unanimity in the literature on whether frequentist and Bayesian approaches are indeed concurrent theories. Thus, a fundamental question arises: frequentist and Bayesian approaches for interval estimation could be somehow reconciled? This paper offers an affirmative response for this question. Furthermore, we introduce a reconciling solution based on a hybrid frequentist-Bayesian interval estimator, the ‘confidence-credible interval’. The hybrid approach is simple and intuitive. It is also comprehensive in the sense of being applicable for any data probability distribution/likelihood shape, and for arbitrary prior distributions. An intensive simulation study shows the performance of the new methodology for the Gaussian and the Gamma distributions. The proposed method is illustrated through an application using real data in the light of state space models.

摘要

如果应用于分析相同的数据集，用于区间估计的频率论和贝叶斯方法通常会产生相互矛盾的结果。矛盾的是，关于频率论和贝叶斯方法是否确实是同时存在的理论，文献中并没有一致意见。因此，出现了一个基本问题：用于区间估计的频率论和贝叶斯方法可以以某种方式协调吗？本文对这个问题给出了肯定的回答。此外，我们引入了一种基于混合频率主义者-贝叶斯区间估计量的协调解决方案，即“置信度-可信区间”。混合方法简单直观。在适用于任何数据概率分布/似然形状和任意先验分布的意义上，它也是全面的。一项深入的模拟研究显示了新方法对高斯和伽马分布的性能。根据状态空间模型，通过使用真实数据的应用程序说明了所提出的方法。