A bayesian approach to the estimation of maps between riemannian manifolds, II: examples

2009/08/18 by Butler, Leo T., Levit, Boris
#Computation (stat.CO) #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.0908.2612

Abstract

Let M be a smooth compact oriented manifold without boundary, imbedded in a euclidean space E and let f be a smooth map of M into a Riemannian manifold N. An unknown state x in M is observed via X=x+su where s>0 is a small parameter and u is a white Gaussian noise. For a given smooth prior on M and smooth estimators g of the map f we have derived a second-order asymptotic expansion for the related Bayesian risk (see arXiv:0705.2540). In this paper, we apply this technique to a variety of examples. The second part examines the first-order conditions for equality-constrained regression problems. The geometric tools that are utilised in our earlier paper are naturally applicable to these regression problems.

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