COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Probability > Learning rates in Bayesian nonparametrics: Gaussian process priors

## Learning rates in Bayesian nonparametrics: Gaussian process priorsAdd to your list(s) Download to your calendar using vCal - Aad van der Vaart (Vrije Univ. Amsterdam)
- Friday 27 November 2009, 16:30-17:30
- MR5, CMS, Wilberforce Road, Cambridge, CB3 0WB.
If you have a question about this talk, please contact Berestycki. This talk has been canceled/deleted Joint with Statistics Series The sample path of a Gaussian process can be used as a prior model for an unknown function that we wish to estimate. For instance, one might model a regression function or log density a priori as the sample path of a Brownian motion or its primitive, or some stationary process. Viewing this prior model as a formal prior distribution in a Bayesian set-up, we obtain a posterior distribution in the usual way, which, given the observations, is a probability distribution on a function space. We study this posterior distribution under the assumption that the data is generated according to some given true function, and are interested in whether the posterior contracts to the true function if the informativeness in the data increases indefinitely, and at what speed. For Gaussian process priors this rate of contraction rate can be described in terms of the small ball probability of the Gaussian process and the position of the true parameter relative to its reproducing kernel Hilbert space. Typically the prior has a strong influence on the contraction rate. This dependence can be alleviated by scaling the sample paths. For instance, an infinitely smooth, stationary Gaussian process scaled by an inverse Gamma variable yields a prior distribution on functions such that the posterior distribution adapts to the unknown smoothness of the true parameter, in the sense that contraction takes place at the minimax rate for the true smoothness. This talk is part of the Probability series. ## This talk is included in these lists:This talk is not included in any other list Note that ex-directory lists are not shown. |
## Other listsIfM Buns Talk Cambridge Global Health Year Plant Sciences Research Seminars## Other talksSingle Cell Seminars (September) The genetic framework of germline stem cell development The Design of Resilient Engineering Infrastructure Systems with Bayesian Networks Modelling discontinuities in simulator output using Voronoi tessellations 160 years of occupational structure: Late Imperial China and its regions Diagnostics and patient pathways in pancreatic cancer The Digital Doctor: Hope, Hype, and Harm at the Dawn of Medicine’s Computer Age XZ: X-ray spectroscopic redshifts of obscured AGN Scale and anisotropic effects in necking of metallic tensile specimens Throwing light on organocatalysis: new opportunities in enantioselective synthesis Towards a whole brain model of perceptual learning Auxin and cytokinin regulation of root architecture - antagonism or synergy |