Ciclo di Seminari - Progetto ERC grant PASCAL (Probabilistic and Statistical Techniques for Cosmological Applications) Lunedì 30 marzo ore 14 - Aula Belpasso - Dipartimento di Matematica Università di Roma Tor Vergata Speaker: Pierpaolo Brutti, Università "La Sapienza" - Roma Title: Estimating the Intrinsic Dimension: The Bayesian way Abstract: In this talk I will first review some of the methods proposed for making inference on the intrinsic dimension of point cloud data sampled from a low-dimensional structure embedded in a high–dimensional ambient space, and then I will describe a Bayesian solution based on a composite likelihood built under working independence assumptions suggested by MacKay and Ghahramani. In order to get a posterior with approximately correct asymptotic behavior and curvature, I will consider some options to calibrate this pseudolikelihood and then compare in simulated and real examples a standard MCMC method against a variation of the default Bayesian framework of Ventura et al. (2013) (joint work with Alessandro Lanteri). Cordiali saluti Claudio Durastanti