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CATEGORIES:SMS Seminars
CONTACT:A/Prof Richard Arnold
DESCRIPTION:Orientations of objects in $\\mathbb{R}^p$ with symmetry group 
 $K$ cannot be described unambiguously by elements of the rotation group $S
 O(p)$\, but correspond instead to elements of the quotient space $SO(p)/K$
 .  Specifications of probability distributions and appropriate statistical
  methods for such objects have been lacking -- with the notable exceptions
  of axial objects in the plane and in $\\mathbb{R}^3$.\n\nWe exploit suita
 ble embeddings of $SO(p)/K$ into spaces of symmetric tensors to provide a 
 systematic and intuitively appealing approach to the statistical analysis 
 of the orientations of such objects.  We firstly consider the case of {\\e
 m orthogonal $r$-frames} in $\\mathbb{R}^p$\, corresponding to sets of $r\
 \leq p$ mutually orthogonal axes in $p$ dimensions\, which includes the Wa
 tson and Bingham distributions.  Using the same approach we then treat the
  three dimensional case of $SO(3)/K$\, where $K$ is one of the point symme
 try groups. In both cases the resulting tools include measures of location
  and dispersion\, tests of uniformity\, one-sample tests for a preferred o
 rientation and two-sample tests for a difference in orientation. The metho
 ds are illustrated using data from earthquake focal mechanisms (fault plan
 e and slip vector orientations) and crystallographic data with orientation
  measurements of distinct mineral phases.
DTEND;TZID=Pacific/Auckland:20190509T170000
DTSTAMP:20260513T202825Z
DTSTART;TZID=Pacific/Auckland:20190509T160000
LOCATION:AM101\, Alan MacDiarmid 101
ORGANIZER:A/Prof Richard Arnold
SUMMARY:A/Prof Richard Arnold - Statistics of Ambiguous Rotations
UID:seminar_sms950_20190506071256
URL:
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