دانلود کتاب A Bayesian Approach to the Estimation of Maps between Riemannian Manifolds

Name: A Bayesian Approach to the Estimation of Maps between Riemannian Manifolds
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Author: Butler L. T.

by Butler L. T., Levit B.

عنوان فارسی: روش بیزی برای برآورد نقشه ها بین ریمانی منیفولد
سال: 2007
زبان: انگلیسی
تعداد صفحه (نسخه چاپی - نسخه الکترونیکی): 17-17
نوع فایل: PDF دانلود نرم افزار مطالعه
حجم: 0.78 مگابایت

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Let be a smooth compact oriented manifold without boundary, imbedded in a Euclidean space , and let be a smooth map of into a Riemannian manifold Λ. An unknown state is observed via X = , where > 0 is a small parameter and is a white Gaussian noise. For a given smooth prior on and smooth estimators of the map we derive a secondorder asymptotic expansion for the related Bayesian risk. The calculation involves the geometry ofthe underlying spaces and , in particular, the integration-by-parts formula. Using this result, a second-order minimax estimator of is found based on the modern theory of harmonic maps and hypo-elliptic differential operators.