Bayesian analysis of Birnbaum–Saunders distribution with partial information

In Bayesian analysis with objective priors, it should be justified that the posterior distribution is proper. In this paper, we show that the reference prior (or independent Jeffreys prior) of a two-parameter Birnbaum–Saunders distribution will result in an improper posterior distribution. However, the posterior distributions are proper based on the reference priors with partial information (RPPI). Based on censored samples, slice sampling is utilized to obtain the Bayesian estimators based on RPPI. Monte Carlo simulations are used to compare the efficiencies of different RPPIs, to assess the sensitivity of the choice of the priors, and to compare the Bayesian estimators with the maximum likelihood estimators, for various scales of sample size and degree of censoring. A real data set is analyzed for illustrative purpose.