Framework for the comparison of <i>a priori</i> and <i>a posteriori</i> error variance estimation and tuning schemes
Bibliographic record
Abstract
Abstract The performance of an assimilation system is strongly dependent on the quality of the error statistics used. A number of error statistics estimation and tuning methods have previously been developed to better assess and determine these statistics. Many of these are a posteriori methods which make use of quantities calculated during the assimilation procedure, while other a priori methods do not require information from the assimilation. In this study, we develop a conceptual framework that relates these methods when applied to error variance determination, where each method is associated with the minimization of a particular cost function. The minimization of these cost functions describes a fitting procedure that fits parts of the prescribed modelled innovation covariance to its observed values. Each method must in some way separate the innovation covariance into its contributions from the background and the observations, which are then used in the fitting procedure. It is shown that the examined a posteriori methods use the analysis filter to make this separation and that the minimization of their associated cost functions is done implicitly within the tuning procedure. Analytical expressions for the expectation value and variance of estimates for error variance scaling parameters are determined for each method. The expressions for the expectation values of these estimates show that the accuracy of each method is dependent on its ability to separate the background from the observation contributions to the innovation covariance. This separability is quantified by use of the Frobenius inner product between the background‐ and observation‐error covariances, which additionally allows for geometric interpretations of the covariances to be made. Comparisons between variance parameter estimates from different methods are made for the case of a 1D periodic domain.
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.
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 | 0.008 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".