How proper are Bayesian models in the astronomical literature?

Understand

The well-known Bayes theorem assumes that a posterior distribution is a probability distribution.

• However, the posterior distribution may no longer be a probability distribution if an improper prior distribution (non-probability measure) such as an unbounded uniform prior is used.
• Improper priors are often used in the astronomical literature to reflect a lack of prior knowledge, but checking whether the resulting posterior is a probability distribution is sometimes neglected.
• It turns out that 23 articles out of 75 articles (30.7%) published online in two renowned astronomy journals (ApJ and MNRAS) between Jan 1, 2017 and Oct 15, 2017 make use of Bayesian analyses without rigorously establishing posterior propriety.