Post-Corrected Raw-Score Martingale Posterior Sampling for von Mises-Fisher Models
Abstract
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.
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BibTeX
@misc{xu2026postcorrected,
title = {{Post-Corrected Raw-Score Martingale Posterior Sampling for von Mises-Fisher Models}},
author = {Yi Xu and Xinye Chen and Sheng Jiang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05096},
eprint = {2609.05096},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05096},
}
RIS
TY - UNPB
TI - Post-Corrected Raw-Score Martingale Posterior Sampling for von Mises-Fisher Models
AU - Yi Xu
AU - Xinye Chen
AU - Sheng Jiang
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05096
UR - https://arxiv.org/abs/2609.05096
AB - 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.
ER -