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X-WR-CALNAME:Department of Statistics and Operations Research
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X-WR-CALDESC:Events for Department of Statistics and Operations Research
BEGIN:VEVENT
DTSTART;TZID=UTC-4:20170327T153000
DTEND;TZID=UTC-4:20170327T163000
DTSTAMP:20170328T022744
CREATED:20170126T140445Z
LAST-MODIFIED:20170126T141711Z
UID:2613-1490628600-1490632200@stat-or.unc.edu
SUMMARY:Hotelling Lectures: Aad van der Vaart\, Leiden University
DESCRIPTION:Nonparametric Bayesian methods: frequentist analysis\nAad van der Vaart\nLeiden University\n\nWe present an overview of Bayesian methods to estimate functions or high-dimensional\nparameter vectors\, and discuss the validity (or not) of these methods from a\nnon-Bayesian point of view. For instance\, we consider using a Gaussian process\nas a prior for a regression function or (after exponentiation and normalisation) for a\ndensity function. We characterise the rate at which the corresponding posterior distribution\ncan recover a true function as the noise level tends to zero or the number of observations tends to infinity\,\nand discuss how this rate can be improved by scaling the time axis\, showing that an appropriate random\nscaling leads to adaptive recovery over a scale of smoothness levels. Recovery means that the posterior\ndistribution concentrates most of its mass near the parameter that generates the data\, for most\nobservations. It refers mostly to the location of the posterior distribution. A second use of the\nposterior distribution is uncertainty quantification\, and refers to the spread of the posterior distribution. In fact\,\nit is at the core of the Bayesian method to use the full posterior distribution as an indication\nof remaining uncertainty. We discuss the general difficulties of uncertainty quantification in\nnonparametric statistics\, from which Bayesian methods of course also cannot escape. We argue that\nthese difficulties imply that the uncertainty quantification of adaptive Bayesian methods must\nbe misleading for certain true parameters\, and present concrete examples.\nWe next show that for so-called self-similar parameters the uncertainty quantification is valid.\n\nThe first talk is a general introduction to these aspects of nonparametric Bayesian\nstatistics\, focused mostly at curve estimation. In the second talk we also address\nsimilar issues in the Bayesian recovery of regression parameters in sparse high-dimensional models.\n\nA reception will follow at 4:30PM in the 3rd floor lounge of Hanes Hall.
URL:http://stat-or.unc.edu/event/hotelling-lectures-aad-van-der-vaart-leiden-university
CATEGORIES:Hotelling Lectures
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