In this paper, we propose a novel intrinsic wrapped Gaussian process regression model for response variable measured on Riemannian manifold. We apply the parallel transport operator to define an intrinsic covariance structure addressing a critical aspect of constructing a well defined Gaussian process regression model. We show that the posterior distribution of regression function is invariant to the choice of orthonormal frames for the coordinate representations of the covariance function. This method can be applied to data situated not only on Euclidean submanifolds but also on manifolds without a natural ambient space. The asymptotic properties for estimating the posterior distribution is established. Numerical studies, including simulation and real-world examples, indicate that the proposed method delivers strong performance.

翻译：本文提出了一种新颖的内蕴卷绕高斯过程回归模型，用于处理黎曼流形上测量的响应变量。我们应用平行移动算子来定义内蕴协方差结构，解决了构建明确定义的高斯过程回归模型的一个关键问题。我们证明了回归函数的后验分布对协方差函数坐标表示的正交标架选择具有不变性。该方法不仅适用于欧几里得子流形上的数据，也可应用于没有自然嵌入空间的流形。我们建立了估计后验分布的渐近性质。数值研究（包括仿真和实际案例）表明，所提方法具有优越的性能。