In the context of Bayesian statistics, we investigate the question of merging of opinions: starting from different priors and observing the same data, will there be convergence between the posterior distributions as more data are coming? And if yes, is it possible to quantify at which rate? This question is delicate in Bayesian Nonparametrics because prior and posterior distributions are typically infinite dimensional, making already the definition of a distance between priors and posteriors a challenge. We concentrate on normalized completely random measures and propose, both a priori and a posteriori: (i) an analysis of their identifiability, (ii) the definition of an optimal transport distance based on their Lévy intensities and (iii) techniques to conduct posterior analyses to study merging of opinions obtaining both finite sample and asymptotic behavior of our distance.
This is joint work with Marta Catalano.
