A Necessary Bayesian Nonparametric Test for Assessing Multivariate Normality
Why this work is in the frame
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Bibliographic record
Abstract
A novel Bayesian nonparametric test for assessing multivariate normal models is presented. Although there are extensive frequentist and graphical methods for testing multivariate normality, it is challenging to find Bayesian counterparts. The approach considered in this paper is based on the Dirichlet process and the squared radii of observations. Specifically, the squared radii are employed to transform the $$m$$ -variate problem into a univariate problem by relying on the fact that if a random sample is coming from a multivariate normal distribution then the square radii follow a particular beta distribution. While the Dirichlet process is used as a prior on the distribution of the square radii, the concentration of the distribution of the Anderson–Darling distance between the posterior process and the beta distribution is compared to that between the prior process and beta distribution via a relative belief ratio. Key results of the approach are derived. The procedure is illustrated through several examples, in which it shows excellent performance.
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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 | 0.115 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it