A Bayesian Approach to the Estimation of Maps between Riemannian Manifolds, Ii: Examples
نویسندگان
چکیده
Abstract. Let Θ be a smooth compact oriented manifold without boundary, imbedded in a euclidean space E, and let γ be a smooth map of Θ into a Riemannian manifold Λ. An unknown state θ ∈ Θ is observed via X = θ + ǫξ where ǫ > 0 is a small parameter and ξ is a white Gaussian noise. For a given smooth prior λ on Θ and smooth estimators g(X) of the map γ we have derived a second-order asymptotic expansion for the related Bayesian risk [3]. 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 [3] are naturally applicable to these regression problems.
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