论文标题
客观贝叶斯分析伽马分布的差分熵
Objective Bayesian Analysis for the Differential Entropy of the Gamma Distribution
论文作者
论文摘要
本文引入了完全客观的贝叶斯分析，以获得熵措施的后验分布。值得注意的是，我们考虑了伽马分布，该分布描述了物理，工程和生物学中许多自然现象。我们根据熵对模型进行修复，并得出不同的客观先验，例如Jeffreys Prior，参考先验和匹配先验。由于所获得的先验是不当的，因此我们证明所获得的后验分布是正确的，并且它们各自的后均值是有限的。进行了一项密集的仿真研究以选择先验，该研究可以返回有关偏见，均方根误差和覆盖概率的更好结果。在两个数据集中说明了所提出的方法：第一个与Achaemenid王朝统治期有关，第二个描述了甘蔗收获机中电子组件故障的时间。
The present paper introduces a fully objective Bayesian analysis to obtain the posterior distribution of an entropy measure. Notably, we consider the gamma distribution, which describes many natural phenomena in physics, engineering, and biology. We reparametrize the model in terms of entropy, and different objective priors are derived, such as Jeffreys prior, reference prior, and matching priors. Since the obtained priors are improper, we prove that the obtained posterior distributions are proper and that their respective posterior means are finite. An intensive simulation study is conducted to select the prior that returns better results regarding bias, mean square error, and coverage probabilities. The proposed approach is illustrated in two datasets: the first relates to the Achaemenid dynasty reign period, and the second describes the time to failure of an electronic component in a sugarcane harvest machine.
