Kaniav Kamari (Université Paris-Dauphine): A discussion on Bayesian analysis : Applying Noninformative Priors

In this paper, we discuss Bayesian statistics that is concerned with generating the posterior distribution of the unknown parameters given both the data and some prior density for the parameters. It is of interest to show that Bayesian data analysis is stable relative to different noninformative choices of prior distribution. As cited in [1], there is unintended influence on the posterior for a function of interest caused by noninformative priors on the parameters and according to these authors, this is a problem that “is often ignored in applications of Bayesian inference”. Those authors focussed on four examples and analysed them for a particular choice of prior. Here, we consider these examples and discuss the Bayesian processing of their model assuming di fferent prior choices. The results of our analysis lead us to infer stability in the posterior distribution of all parameters . So, the e ffect of the chosen noninformative prior is essentially void even though there is not something like “non informative” prior.