Likelihood and its use in Parameter Estimation and Model Comparison
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Parameter estimation and model fitting underlie many statistical procedures. Whether the objective is to examine central tendency or the slope of a regression line, an estimation method must be used. Likelihood is the basis for parameter estimation, for determining the best relative fit among several statistical models, and for significance testing. In this review, the concept of Likelihood is explained and applied computation examples are given. The examples provided serve to illustrate how likelihood is relevant, and related to, the most frequently applied test statistics (Student’s t-test, ANOVA). Additional examples illustrate the computation of Likelihood(s) using common population model assumptions (e.g., normality) and alternative assumptions for cases where data are non-normal. To further describe the interconnectedness of Likelihood and the Likelihood Ratio with modern test statistics, the relationship between Likelihood, Least Squares Modeling, and Bayesian Inference are discussed. Finally, the advantages and limitations of Likelihood methods are listed, alternatives to Likelihood are briefly reviewed, and R code to compute each of the examples in the text is provided.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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