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PreprintCC BY 4.0arXiv

Markov chain Monte Carlo for predictively oriented posteriors

  • Yann McLatchie
  • Louis Sharrock
  • David T. Frazier
  • Jeremias Knoblauch
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Abstract

The predictively oriented posterior offers principled uncertainty quantification, even under model misspecification. However, it does not admit an explicit density and therefore cannot be computed using classical Monte Carlo sampling algorithms. We remedy this by deriving an approximation to the predictively oriented posterior whose density can be evaluated point-wise, and whose approximation error decays rapidly. These results are illustrated on case studies from epidemiology, spatial statistics, and low-energy nuclear physics.

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Cite

BibTeXRIS
BibTeX
@misc{mclatchie2026markov,
  title = {{Markov chain Monte Carlo for predictively oriented posteriors}},
  author = {Yann McLatchie and Louis Sharrock and David T. Frazier and Jeremias Knoblauch},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01818},
  eprint = {2610.01818},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01818},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Markov chain Monte Carlo for predictively oriented posteriors
AU  - Yann McLatchie
AU  - Louis Sharrock
AU  - David T. Frazier
AU  - Jeremias Knoblauch
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01818
UR  - https://arxiv.org/abs/2610.01818
AB  - The predictively oriented posterior offers principled uncertainty quantification, even under model misspecification. However, it does not admit an explicit density and therefore cannot be computed using classical Monte Carlo sampling algorithms. We remedy this by deriving an approximation to the predictively oriented posterior whose density can be evaluated point-wise, and whose approximation error decays rapidly. These results are illustrated on case studies from epidemiology, spatial statistics, and low-energy nuclear physics.
ER  -