Estimating a density near an unknown manifold: a Bayesian nonparametric approach

C Berenfeld, P Rosa, J Rousseau - The Annals of Statistics, 2024 - projecteuclid.org
In the supplementary material [8], we present further technical results regarding the
geometric framework and general anisotropic Hölder functions. We also provide …

Lipschitz continuity of probability kernels in the optimal transport framework

E Dolera, E Mainini - arXiv preprint arXiv:2010.08380, 2020 - arxiv.org
In Bayesian statistics, a continuity property of the posterior distribution with respect to the
observable variable is crucial as it expresses well-posedness, ie, stability with respect to …

Statistical inference on unknown manifolds

C Berenfeld - 2022 - theses.hal.science
In high-dimensional statistics, the manifold hypothesis presumes that the data lie near low-
dimensional structures, called manifolds. This assumption helps explain why machine …

Strong posterior contraction rates via Wasserstein dynamics

E Dolera, S Favaro, E Mainini - Probability Theory and Related Fields, 2024 - Springer
In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the
posterior distribution concentrates on arbitrarily small neighborhoods of a true model, in a …