Conditions for interior based constrained prior distributions to ensure probability density

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.

کلیدواژه ها:

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