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A Least-Squares Approach to Sample-Based Prior Elicitation — arXiv:2608.08779

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.08779
License (as archived): CC0-1.0
Archived: 2026-10-19T09:03:25.097Z
SHA-256 of the archived text: 7fc77b53a9cea5e878b0074762509834f26dd04437a3706ad120be97c804b6f9
Stable URL of this page: https://metraipolis.com/documento/dc_8221cb288f3d

How to cite

A Least-Squares Approach to Sample-Based Prior Elicitation — arXiv:2608.08779 — arXiv (en), https://arxiv.org/abs/2608.08779 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_8221cb288f3d (Metraipolis archive dc_8221cb288f3d, sha256 7fc77b53a9cea5e878b0074762509834f26dd04437a3706ad120be97c804b6f9)

BibTeX

@misc{dc8221cb288f3d,
  title = {A Least-Squares Approach to Sample-Based Prior Elicitation — arXiv:2608.08779},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.08779},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_8221cb288f3d; sha256 7fc77b53a9cea5e878b0074762509834f26dd04437a3706ad120be97c804b6f9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.08779. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

An expert who supplies examples of a quantity often also signals how plausible each one is; when is that signal worth using? We study eliciting a Bayesian prior from an expert who provides example points together with their approximate likelihoods. We propose fitting the prior by least squares--minimizing the squared discrepancy between a parametric density and the elicited likelihoods--which defines an M-estimator that remains well posed even for families whose moments do not exist. We establish consistency and asymptotic normality, and prove--under explicit regularity conditions, comprising a well-separation and a uniform-concentration requirement that we verify for the families considered--a non-asymptotic O(1/sqrt(n)) Berry--Esseen bound on its sampling distribution, uniform and nonuniform, by extending a result of Pinelis for maximum-likelihood estimators to the M-estimation setting. We then relax the assumptions that most limit the method in practice. Experts need not report on the density's own scale: an unknown reporting scale can be profiled out in closed form and estimated jointly, at no asymptotic cost for location families. The theory extends to multivariate parameters, where a directional Berry--Esseen bound follows from the multivariate delta method applied to a smooth implicit proxy for the estimator. An additive error floor in the noise model removes a degeneracy in the optimal design, making optimal designs interior. Simulations for normal and beta families confirm the predicted n^-1 error rate and the accuracy of the normal approximation at moderate sample sizes. Finally, we compare the estimator with the sample-only maximum-likelihood baseline, derive an explicit threshold on the expert's reporting noise below which the elicited likelihoods provably reduce estimation error, and calibrate that threshold against eleven datasets of human frequency judgments.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-08-11 in stat.ME).
Categorie arXiv: Methodology (stat.ME) ; Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2608.08779 — 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 2026-10-19T09:02:02.363Z dalla pagina https://arxiv.org/catchup/stat.ME/2026-08-11?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).