Empirical Bayesian Approach to Testing Homogeneity of Several Means of Inflated Poisson Distributions (IPD)
Bibliographic record
Abstract
Objectives: We introduce a special form of the Generalized Poisson Distribution. The distribution has one parameter, yet it has a variance that is larger than the mean a phenomenon known as “over dispersion”. We discuss potential applications of the distribution as a model of counts, and under the assumption of independence we will perform statistical inference on the ratio of two means, with generalization to testing the homogeneity of several means. Methods: Bayesian methods depend on the choice of the prior distributions of the population parameters. In this paper, we describe a Bayesian approach for estimation and inference on the parameters of several independent Inflated Poisson (IPD) distributions with two possible priors, the first is the reciprocal of the square root of the Poisson parameter and the other is a conjugate Gamma prior. The parameters of Gamma distribution are estimated in the empirical Bayesian framework using the maximum likelihood (ML) solution using nonlinear mixed model (NLMIXED) in SAS. With these priors we construct the highest posterior confidence intervals on the ratio of two IPD parameters and test the homogeneity of several populations. Results: We encountered convergence problem in estimating the hyperparameters of the posterior distribution using the NLMIXED. However, direct maximization of the predictive density produced solutions to the maximum likelihood equations. We apply the methodologies to RNA-SEQ read count data of gene expression values.
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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 | 0.032 | 0.109 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".