Objective Bayesian analysis for the differential entropy of the Gamma distribution

Author(s)

Ramos, Eduardo ; Egbon, Osafu A. ; Ramos, Pedro L. ; Rodrigues, Francisco A. ; Louzada, Francisco

• Document type: Journal article
• Source: BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS; v. 38, n. 1, p. 21-pg., 2024-03-01.

Abstract

The 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. (AU)

• FAPESP's process: 19/27636-9 - Posteriori properties for Bayesian regression models and applications in large and complex industrial and medical data
• Grantee: Eduardo Ramos
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC