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Post-Corrected Raw-Score Martingale Posterior Sampling for von Mises-Fisher Models — arXiv:2609.05096

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.05096
License (as archived): CC0-1.0
Archived: 2026-10-16T23:03:15.850Z
SHA-256 of the archived text: 26e071f86fec04a33f495ff9644e862bda7676ec22032a32065a3085cf8e844f
Stable URL of this page: https://metraipolis.com/documento/dc_df11717cab8a

How to cite

Post-Corrected Raw-Score Martingale Posterior Sampling for von Mises-Fisher Models — arXiv:2609.05096 — arXiv (en), https://arxiv.org/abs/2609.05096 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_df11717cab8a (Metraipolis archive dc_df11717cab8a, sha256 26e071f86fec04a33f495ff9644e862bda7676ec22032a32065a3085cf8e844f)

BibTeX

@misc{dcdf11717cab8a,
  title = {Post-Corrected Raw-Score Martingale Posterior Sampling for von Mises-Fisher Models — arXiv:2609.05096},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.05096},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_df11717cab8a; sha256 26e071f86fec04a33f495ff9644e862bda7676ec22032a32065a3085cf8e844f},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.05096. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-09-07 in stat.ME).
Categorie arXiv: Methodology (stat.ME) ; Computation (stat.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.05096 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T22:47:06.812Z dalla pagina https://arxiv.org/catchup/stat.ME/2026-09-07?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).