On Metrizing Vague Convergence of Random Measures with Applications on\n Bayesian Nonparametric Models
Bibliographic record
Abstract
This paper deals with studying vague convergence of random measures of the\nform $\\mu_{n}=\\sum_{i=1}^{n} p_{i,n} \\delta_{\\theta_i}$, where\n$(\\theta_i)_{1\\le i \\le n}$ is a sequence of independent and identically\ndistributed random variables with common distribution $\\Pi$, $(p_{i,n})_{1 \\le\ni \\le n}$ are random variables chosen according to certain procedures and are\nindependent of $(\\theta_i)_{i \\geq 1}$ and $\\delta_{\\theta_i}$ denotes the\nDirac measure at $\\theta_i$. We show that $\\mu_{n}$ converges vaguely to\n$\\mu=\\sum_{i=1}^{\\infty} p_{i} \\delta_{\\theta_i}$ if and only if\n$\\mu^{(k)}_{n}=\\sum_{i=1}^{k} p_{i,n} \\delta_{\\theta_i}$ converges vaguely to\n$\\mu^{(k)}=\\sum_{i=1}^{k} p_{i} \\delta_{\\theta_i}$ for all $k$ fixed. The\nlimiting process $\\mu$ plays a central role in many areas in statistics,\nincluding Bayesian nonparametric models. A finite approximation of the beta\nprocess is derived from the application of this result. A simulated example is\nincorporated, in which the proposed approach exhibits an excellent performance\nover several existing algorithms.\n
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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 | 0.096 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.002 | 0.009 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.003 | 0.007 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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.
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".