Probabilistic approaches to geometric statistics

Stochastic processes, transition distributions, and fiber bundle geometry

Stefan Sommer    University of Copenhagen, Department of Computer Science, Copenhagen, Denmark


We discuss construction of parametric families of intrinsically defined and geometrically natural probability distributions on manifolds, in particular, how to generalize the Euclidean normal distribution. This opens up for probabilistic formulations of concepts such as the mean value, covariance, and principal component analysis and general likelihood-based inference. The general idea is to use transition distributions of stochastic processes on manifolds to construct probabilistic models. For manifolds with connection, ...

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