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Record W4411370832 · doi:10.31219/osf.io/wzqxg_v3

Bayesian estimation in multiple comparisons

2025· preprint· en· W4411370832 on OpenAlex
Guilherme D. Garcia

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

fundA Canadian funder is recorded on the work.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

Venuenot available
Typepreprint
Languageen
FieldMathematics
TopicStatistical Methods and Bayesian Inference
Canadian institutionsnot available
FundersSocial Sciences and Humanities Research Council of CanadaUniversité Laval
KeywordsEstimationBayesian probabilityBayes estimatorEconometricsStatisticsComputer scienceArtificial intelligenceMathematicsEconomics

Abstract

fetched live from OpenAlex

Traditional regression models typically estimate parameters for a factor F by designating one level as a reference (intercept) and calculating slopes for other levels of F. While this approach often aligns with our research question(s), it limits direct comparisons between all pairs of levels within F and requires additional procedures for generating these comparisons. Moreover, Frequentist methods often rely on corrections (e.g., Bonferroni or Tukey), which can reduce statistical power and inflate uncertainty by mechanically widening confidence intervals. This paper demonstrates how Bayesian hierarchical models provide a robust framework for parameter estimation in the context of multiple comparisons. By leveraging entire posterior distributions, these models produce estimates for all pairwise comparisons without requiring post hoc adjustments. The hierarchical structure, combined with the use of priors, naturally incorporates shrinkage, pulling extreme estimates toward the overall mean. This regularization improves the stability and reliability of estimates, particularly in the presence of sparse or noisy data, and leads to more conservative comparisons. Bayesian models also offer a flexible framework for addressing heteroscedasticity by directly modeling variance structures and incorporating them into the posterior distribution. The result is a coherent approach to exploring differences between levels of F, where parameter estimates reflect the full uncertainty of the data.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.003
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.375
Threshold uncertainty score0.834

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.003
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.119
GPT teacher head0.419
Teacher spread0.300 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it