Amirhossein Ghatari - Department of Statistics‎, ‎Amirkabir University of Technology‎, ‎Tehran‎, ‎Iran
Elham Tabrizi - Department of Mathematics‎, ‎Kharazmi University‎, ‎Tehran‎, ‎Iran

In Bayesian inference‎, ‎the acquisition of prior distributions plays a fundamental role‎. ‎While authorized priors need not conform to traditional probability densities and may be improper priors‎, ‎obtaining proper prior densities remains a challenge in the Bayesian literature‎. ‎This article explores a set of conditions that enable the establishment of specific assumptions‎, ‎ensuring that maximum entropy priors and restricted reference priors become proper and transform into probability density priors‎. ‎By examining these conditions‎, ‎this study contributes to the advancement of proper prior acquisition in Bayesian analysis.

Constrained prior, Jensen inequality, Maximum entropy prior, Restricted reference priors