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 distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.007 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.004 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".