Information geometry and prior selection
Hichem Snoussi · AIP conference proceedings · 2003
In this contribution, we study the problem of prior selection arising in Bayesian inference. There is an extensive literature on the construction of non informative priors and the subject seems far from a definite solution [1]. Here we revisit this subject with differential geometry tools and propose to construct the prior in a Bayesian decision theoretic framework. We show how the construction of a prior by projection is the best way to take into account the restriction to a particular family of parametric models. For instance, we apply this procedure to the curved parametric families where the ignorance is directly expressed by the relative geometry of the restricted model in the wider model containing it.