Bayesian Inference for the Intrinsic Dimension

In this work we propose a new Bayesian method for making in- ference on the intrinsic dimension of point cloud data sampled from a low– dimensional structure embedded in a high–dimensional ambient space. The basic ingredient of our Bayesian recipe is a composite marginal likelihood built under working independence assumptions, that was suggested by MacKay and Ghahramani [6] to improve on an earlier proposal based on local Poisson process approximations (see [5]). In order to get a posterior with approximately correct asymptotic behavior and curvature, we calibrate this pseudolikelihood as in [8] and then compare in simulated and real exam- ples a standard MCMC method against a variation of the default Bayesian framework described in [12].