发帖
雷达卡
摘要翻译：
设θ是嵌入在欧几里得空间中的光滑紧致定向流形，设γ是θ到黎曼流形λ的光滑映射。通过x=θ+εxi观察到一个未知态θinθ，其中ε>0是一个小参数，\xi是一个高斯白噪声。对于给定的映射γ的光滑先验和光滑估计，我们得到了相关贝叶斯风险的二阶渐近展开式。计算涉及到底层空间θ和λ的几何，特别是逐部分积分公式。利用这一结果，在现代调和映射理论和次椭圆微分算子的基础上，得到了\γ的二阶极大极小估计。
---
英文标题：
《A Bayesian approach to the estimation of maps between riemannian
manifolds》
---
作者：
Leo T. Butler, Boris Levit
---
最新提交年份：
2008
---
分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
--
一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
--
---
英文摘要：
Let \Theta be a smooth compact oriented manifold without boundary, embedded in a euclidean space and let \gamma be a smooth map \Theta into a riemannian manifold \Lambda. An unknown state \theta \in \Theta is observed via X=\theta+\epsilon \xi where \epsilon>0 is a small parameter and \xi is a white Gaussian noise. For a given smooth prior on \Theta and smooth estimator g of the map \gamma we derive a second-order asymptotic expansion for the related Bayesian risk. The calculation involves the geometry of the underlying spaces \Theta and \Lambda, in particular, the integration-by-parts formula. Using this result, a second-order minimax estimator of \gamma is found based on the modern theory of harmonic maps and hypo-elliptic differential operators.
---
PDF链接：
https://arxiv.org/pdf/705.254
京公网安备 11010802022788号
