  Following the critical review of Seaman et al. (2012), we reflect on what is
presumably the most essential aspect of Bayesian statistics, namely the
selection of a prior density. In some cases, Bayesian inference remains fairly
stable under a large range of noninformative prior distributions. However, as
discussed by \citet{Hd}, there may also be unintended consequences of a choice
of a noninformative prior and, these authors consider this problem ignored in
Bayesian studies. As they based their argumentation on four examples, we
reassess these examples and their Bayesian processing via different prior
choices. Our conclusion is to lower the degree of worry about the impact of the
prior, exhibiting an overall stability of the posterior distributions. We thus
consider that the warnings of Seaman et al. (2012), while commendable, do not
jeopardize the use of most noninformative priors.
