有限混合分布的詹森 - 费希尔、费希尔和贝叶斯 - 费希尔信息度量的离散版本

Discrete Versions of Jensen-Fisher, Fisher and Bayes-Fisher Information Measures of Finite Mixture Distributions.

作者信息

Kharazmi Omid, Balakrishnan Narayanaswamy

机构信息

Department of Statistics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O. Box 518, Rafsanjan, Iran.

Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada.

出版信息

Entropy (Basel). 2021 Mar 18;23(3):363. doi: 10.3390/e23030363.

DOI:10.3390/e23030363

PMID:33803766

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8003337/

Abstract

In this work, we first consider the discrete version of Fisher information measure and then propose Jensen-Fisher information, to develop some associated results. Next, we consider Fisher information and Bayes-Fisher information measures for mixing parameter vector of a finite mixture probability mass function and establish some results. We provide some connections between these measures with some known informational measures such as chi-square divergence, Shannon entropy, Kullback-Leibler, Jeffreys and Jensen-Shannon divergences.

摘要

在这项工作中，我们首先考虑费希尔信息度量的离散版本，然后提出詹森 - 费希尔信息，以得出一些相关结果。接下来，我们针对有限混合概率质量函数的混合参数向量考虑费希尔信息和贝叶斯 - 费希尔信息度量，并建立一些结果。我们给出了这些度量与一些已知信息度量之间的一些联系，如卡方散度、香农熵、库尔贝克 - 莱布勒散度、杰弗里斯散度和詹森 - 香农散度。