Random Matrices - Geometric Methods Working Group

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Announcements

Meeting Time: Thurdsay, 3:00-5:00
Location: NISS building, Room 201

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Theme of research

Distribution on covariance manifolds;

Inference/tracking of time-varying structures;

Statistical shape analysis.

Announcements :

On December 14, Donald Richards will speak about his research.
Title: Minimax estimation for the deconvolution problem over the space of positive definite matrices.
Abstract: We consider the problem of statistical deconvolution on the space of positive definite matrices. This problem is motivated by diffusion tensor image analysis, and the error analyses which are necessary to solve the inverse problem of recontructing true brain images through diffusion tensor inaging.
In January 2007, there will be a course on Geometry, Random matrices and Statistical Inference , as well as a workshop from January 16-19.

Meeting Activities

Date	Topics & Readings	Notes
09/28/06	Discussion on the problem of statistics on multivariate distributions with an application to diffusion tensor Magnetic Resonance Imaging: geometry of p.d. matrices as a convex cone	Statistics on Multivariate Normal Distributions: A Geometric Approach and its Application to Diffusion Tensor MRI
	geometric subspace tracking, setting up a sequential Monte Carlo procedure for inference (to be discussed later)	Bayesian, Geometric Subspace Tracking
10/05/06	Discussion continued on the geometry of p.d. matrices as a convex cone .	A differential geometric approach to the geometric mean of symetric positive-definite matrices, MAHER MOAKHER, SIAM J.MATRIX ANAL.APPL. VOL 26, No. 3, pp. 735-747
10/12/06	Discussion on Moakher's paper	Makram's draft , Smartboard notes
10/19/06	Discussion on positive definite matrices : paper 1, paper 2	Smartboard notes
11/16/06	Discussion on the application of the logarithm distance to statistics in shrinking. Discussion on Principle Geodesic analysis : paper 1, paper 2	Smartboard notes
11/30/06	Talk by Armin Scwartzman : Probability Distributions for Positive Definite Matrices.	Donald's comments : Smartboard notes
12/07/06	Talk by Hongtu Zhu : Statistical Analysis of Diffusion Tensors in Diffusion-weighted Magnetic Resonance Image Data

Group Members

Name	Affiliation	Email Address
Carlos Carvalho	Duke	carlos (at) stat.duke.edu
Ginger Davis	UVA	gingerdavis (at) virginia.edu
Thomas Guhr	Lund Institute of Technology	Thomas.Guhr (at) matfys.lth.se
Helene Massam	York University	massamh (at) yorku.ca
Jing Naihuan	N.C. State	jing (at) math.ncsu.edu
Jayanta Pal	SAMSI	jpal (at) samsi.info
Bala Rajaratnam	SAMSI	br62 (at) samsi.info
Igor Rumanov	UC-Davis	igorrumanov (at) math.ucdavis.edu
Armin Schwartzman	Harvard School of Public Health	armins (at) hsph.harvard.edu
Steven Smith	M.I.T. Lincoln Laboratory	stsmith(at) ll.mit.edu
Makram Talih	Hunter College, CUNY	talih (at) math.hunter.cuny.edu
Craig Tracy	UC-Davis	tracy (at) math.ucdavis.edu