The Bayesian method of moments (BMOM) in some aggregation problems in econometrics
Bibliographic record
Abstract
Abstract The BMOM is particularly useful for obtaining post‐data moments and densities for parameters and future observations when the form of the likelihood function is unknown and thus a traditional Bayesian approach cannot be used. Also, even when the form of the likelihood is assumed known, in time series problems it is sometimes difficult to formulate an appropriate prior density. Here, we show how the BMOM approach can be used in two, nontraditional problems. The first one is conditional forecasting in regression and time series autoregressive models. Specifically, it is shown that when forecasting disaggregated data (say quarterly data) and given aggregate constraints (say in terms of annual data) it is possible to apply a Bayesian approach to derive conditional forecasts in the multiple regression model. The types of constraints (conditioning) usually considered are that the sum, or the average, of the forecasts equals a given value. This kind of condition can be applied to forecasting quarterly values whose sum must be equal to a given annual value. Analogous results are obtained for AR(p) models. The second problem we analyse is the issue of aggregation and disaggregation of data in relation to predictive precision and modelling. Predictive densities are derived for future aggregate values by means of the BMOM based on a model for disaggregated data. They are then compared with those derived based on aggregated data. Copyright © 2006 John Wiley & Sons, Ltd.
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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 | 0.011 | 0.034 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| 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".