AI 中文总结
本文针对冯·米塞斯-费舍尔模型开发了后校正原始得分鞅后验采样方法，通过分离预测模拟与协方差校准并引入混合版本，经理论证明与模拟验证可有效降低截断欠离散，适用于方向不确定性分析。
AI 中文摘要
我们针对原始得分鞅后验开发了一种有限时间范围校准方法，并以冯·米塞斯-费舍尔（von Mises–Fisher）模型作为主要示例。从最大似然估计出发，通过从当前拟合模型模拟未来观测值并利用未预处理得分增量更新自然参数，生成预测路径。核心方法步骤是将预测模拟与协方差校准分离：原始得分增量具有费舍尔信息协方差，而伯恩斯坦-冯·米塞斯（Bernstein–von Mises）校准需要逆信息协方差，因此我们基于局部信息估计应用了终端线性校正。为实现更高效的实现，我们还引入了混合版本，用匹配主导阶二次变差的高斯近似替代无限预测延续的省略尾部。我们证明了固定n收敛性、高斯尾部的有限时间范围近似界，以及混合后校正采样器在局部正则性和一致终端校准下的伯恩斯坦-冯·米塞斯极限。模拟结果显示，尾部校正可减少截断导致的欠离散，而OSCAR洋流示例则说明了局部方向不确定性摘要。
英文摘要
We develop a finite-horizon calibration method for raw-score martingale posteriors, with von Mises--Fisher models as the main worked example. Starting from the maximum likelihood estimator, predictive paths are generated by simulating future observations from the current fitted model and updating the natural parameter by unpreconditioned score increments. The main methodological step is to separate predictive simulation from covariance calibration. Raw-score increments have Fisher-information covariance, whereas Bernstein--von Mises calibration requires inverse-information covariance. We therefore apply a terminal linear correction based on a local information estimate. For more efficient implementation, we also introduce a hybrid version that replaces the omitted tail of the infinite predictive continuation by a Gaussian approximation with matching leading-order quadratic variation. We prove fixed-n convergence, a finite-horizon approximation bound for the Gaussian tail, and a Bernstein--von Mises limit for the hybrid post-corrected sampler under local regularity and consistent terminal calibration. Simulations show that tail correction reduces truncation-induced underdispersion, and an OSCAR ocean-current example illustrates local directional uncertainty summaries.
