Bayesian Prediction Regions and Density Estimation With Type-2 Censored Data
Bibliographic record
Abstract
For exponentially distributed lifetimes, we consider the prediction of future order statistics based on having observed the first$m$-order statistics. We focus on the previously less explored aspects of predicting: 1) an arbitrary pair of future order statistics, such as the next and last ones, as well as 2) the next$N$future order statistics. We provide explicit and exact Bayesian credible regions associated with Gamma priors, and constructed by identifying a region with a given credibility$1-\lambda$under the Bayesian predictive density. For (2), the highest posterior density region is obtained, while a two-step algorithm is given for (1). The predictive distributions are represented as mixtures of bivariate Pareto distributions, as well as multivariate Pareto distributions. For the noninformative prior density choice, we demonstrate that a resulting Bayesian credible region has matching frequentist coverage probability, and that the resulting predictive density possesses the optimality properties of best invariance and minimaxity.
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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 | 0.030 | 0.164 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.004 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.005 | 0.008 |
| Open science | 0.008 | 0.004 |
| Research integrity | 0.004 | 0.007 |
| Insufficient payload (model declined to judge) | 0.008 | 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".