Large variance Gaussian priors in Bayesian nonparametric estimation: a maxiset approach

25 pagesInternational audienceIn this paper we compare wavelet Bayesian rules taking into account the sparsity of the signal with priors which are combinations of a Dirac mass with a standard distribution properly normalized. To perform these comparisons, we take the maxiset point of view: i. e. we consider the set of functions which are well estimated (at a prescribed rate) by each procedure. We especially consider the standard cases of Gaussian and heavy-tailed priors. We show that if heavy-tailed priors have extremely good maxiset behavior compared to traditional Gaussian priors, considering large variance Gaussian priors (LVGP) leads to equally successful maxiset behavior. Moreover, these LVGP can be constructed in an adaptive way. We also show, using comparative simulations results that large variance Gaussian priors have very good numerical performances, confirming the maxiset prediction, and providing the advantage of a high simplicity from the computational point of view