Bayesian consensus‐based sample size criteria for binomial proportions
Bibliographic record
Abstract
Many sample size criteria exist. These include power calculations and methods based on confidence interval widths from a frequentist viewpoint, and Bayesian methods based on credible interval widths or decision theory. Bayesian methods account for the inherent uncertainty of inputs to sample size calculations through the use of prior information rather than the point estimates typically used by frequentist methods. However, the choice of prior density can be problematic because there will almost always be different appreciations of the past evidence. Such differences can be accommodated a priori by robust methods for Bayesian design, for example, using mixtures or ϵ-contaminated priors. This would then ensure that the prior class includes divergent opinions. However, one may prefer to report several posterior densities arising from a "community of priors," which cover the range of plausible prior densities, rather than forming a single class of priors. To date, however, there are no corresponding sample size methods that specifically account for a community of prior densities in the sense of ensuring a large-enough sample size for the data to sufficiently overwhelm the priors to ensure consensus across widely divergent prior views. In this paper, we develop methods that account for the variability in prior opinions by providing the sample size required to induce posterior agreement to a prespecified degree. Prototypic examples to one- and two-sample binomial outcomes are included. We compare sample sizes from criteria that consider a family of priors to those that would result from previous interval-based Bayesian criteria.
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.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.135 | 0.444 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.003 |
| Bibliometrics | 0.006 | 0.003 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.006 | 0.005 |
| Research integrity | 0.005 | 0.006 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".