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Statistics for geometric data and applications to anthropology

Statistics for geometric data and applications to anthropology

 

Many modern imaging techniques, such as CT and MRI, produce highly structured observations known as geometric data. These types of data are used in a variety of scientific disciplines, including in anthropology, computational anatomy, kinesiology, and neuroscience. A key challenge in the statistical analysis of such data is their inherent nonlinear structure; one cannot add, subtract, or multiply geometric shapes while guaranteeing that the result is of the same type of shape. This is problematic because most standard statistical procedures rely heavily on this type of linearity. In practice, this problem is either ignored, partially mitigated by choosing good linearizations, or, ideally, avoided by using fully non-linear methods. Unfortunately, the last approach is often underdeveloped when compared to the needs of scientists and practitioners. In this international collaboration, we address this challenge, building on our joint expertise in geometry and statistics, as well as our experience in anthropological applications. We will develop new statistical tools and investigate tradeoffs between existing methods such as principal component analysis, regression, and dimension reduction. A particular focus will be on data consisting of geometric surfaces due to their high importance in anthropology.

 


Organisers

 

JProf. Dr. Philipp Harms
Department Mathematical Stochastics
University of Freiburg

Email philipp.harms@stochastik.uni-freiburg.de
Homepage http://www.philippharms.com/

 

Prof. Matthew Reimherr
Department Statistics
PennState University

Email
Homepage http://www.personal.psu.edu/mlr36/