Bayesian duality and risk analysis on the statistical manifold of exponential family with censored data
作者：
Highlights：
•
• The reliability function of the exponential family is defined in a more general form.
• The dual coordinate system and dual function are obtained. Then the dualistic structure on the manifold is derived.
• The maximum likelihood estimate (MLE) is obtained by minimizing the Bregman divergence.
• The Bayesian duality on the manifold is investigated, and the Bayesian estimators are provided.
• Take gamma distribution as an example, we give the exact results for the dual coordinate system and dual function.
摘要
•The reliability function of the exponential family is defined in a more general form.•The dual coordinate system and dual function are obtained. Then the dualistic structure on the manifold is derived.•The maximum likelihood estimate (MLE) is obtained by minimizing the Bregman divergence.•The Bayesian duality on the manifold is investigated, and the Bayesian estimators are provided.•Take gamma distribution as an example, we give the exact results for the dual coordinate system and dual function.
论文关键词：53B05,60E05,62N05,Bayesian duality,Statistical manifold,Risk analysis,Bregman divergence,Censored data
论文评审过程：Received 12 May 2017, Revised 16 October 2017, Available online 24 April 2018, Version of Record 16 May 2018.
论文官网地址：https://doi.org/10.1016/j.cam.2018.03.043
