Revista de Matemática Aplicada e Computacional

Reflecting About Selecting Noninformative Priors

Abstract

Kamary K and Robert CP

Following the critical review of Seaman et al., we react on an essential aspect of Bayesian statistics, namely the selection of a prior density. In some cases, Bayesian data analysis remains stable under different choices of noninformative prior distributions. However, as discussed by Seaman et al., there may also be unintended consequences of a choice of noninformative prior and, according to these authors, this is a problem often ignored in applications of Bayesian inference". They focused on four examples, analyzing each for several choices of prior. Here, we reassess these examples and their Bayesian processing via different prior choices for fixed data sets. The conclusion is to infer the overall stability of the posterior distributions and to consider that the effect of reasonable noninformative priors is mostly negligible.