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VERSION:2.0
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CALSCALE:GREGORIAN
X-WR-CALNAME:Statistics Department Research Seminar
X-WR-TIMEZONE:Pacific Time (US & Canada)
BEGIN:VEVENT
DTSTAMP:20261010T203101Z
UID:tag:localist.com\,2008:EventInstance_4384678
DTSTART:20190225T235500Z
DTEND:20190226T000000Z
DESCRIPTION:Speaker: Luis Tenoroio\, Ph.D.\, Associate Professor in Applied
  Mathematics and Statistics at Colorado School of Mines.\n\nTopic: Optimal
  low-rank approximations for Bayesian linear inverse problems\n\nAbstract:
  In the Bayesian approach to large-scale inverse problems data are informa
 tive relative to the prior only on a low-dimensional subspace of the param
 eter space. We propose optimal dimensionality reduction techniques for the
  solution of linear–Gaussian inverse problems that can focus on a quanti
 ty of interest (QoI) (a function of the inversion parameters). We study th
 e approximation of the posterior covariance of the QoI as low-rank negativ
 e updates of its prior covariance\, and prove optimality of this update wi
 th respect to a natural geodesic distance on the manifold of symmetric pos
 itive definite matrices first proposed by Rao. Assuming exact knowledge of
  the posterior mean of the QoI\, the optimality results extend to optimali
 ty in distribution with respect to the Kullback-Leibler divergence and the
  Hellinger distance between the associated distributions. We also propose 
 the approximation of the posterior mean of the QoI as a low-rank linear fu
 nction of the data\, and prove optimality of this approximation with respe
 ct to a weighted Bayes risk. These optimal approximations do not require t
 he explicit computation of the full posterior distribution of the paramete
 rs and focus instead on directions that are well informed by the data and 
 are relevant to the QoI.
GEO:44.567164;-123.278692
LOCATION:Kelley Engineering Center\, Room 1001
SUMMARY:Statistics Department Research Seminar
URL;VALUE=URI:https://events.oregonstate.edu/event/statistics_department_re
 search_seminar_2631
CATEGORIES:Lecture or Presentation
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