Mathematics, Systems and Robotics Seminar  RSS

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07/11/2003, 15:00 — 16:00 — Room P3.31, Mathematics Building
João Xavier and Diogo Gomes, ISR/IST and CAM/IST

"Lower Bound on Intrinsic Variance of Estimators in Riemannian Manifolds" and "Optimal Mass Transport"

  • João Xavier - Lower Bound on Intrinsic Variance of Estimators in Riemannian Manifolds

    Abstract: The well-known Cramér-Rao inequality places a lower bound on the variance of any unbiased estimator for a given parametric estimation problem. In the original formulation, the parameter set is an open set of a (flat) Euclidean space. Here, we discuss a generalization of the CR -bound for the case where the parameter set is a Riemannian manifold M and the variance of the estimators is computed with respect to the geodesic distance on M . The derived bound depends on the curvature of the manifold M and differential-geometric generalizations of both the estimator bias and the Fisher information matrix of the parametric model. Numerical examples are presented to illustrate the tightness of the bound.

  • Diogo Gomes - Optimal Mass Transport

    Abstract: We present the optimal transport problem and discuss several of its applications to image identification, shape optimization and nonlinear diffusions.

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