Estimation of Instrument Variance and Bias Using Bayesian Methods
Bibliographic record
Abstract
Imprecision of sensors is one of the main causes of poor control and process performance. Often, instrument measurement bias and variance change over the time and online calibration/re-estimation is necessary. Originated from a real industrial application problem, this paper proposed a Bayesian approach to determine the inconsistency of sensors, based on mass-balance principles. A mass-balance factor model is then introduced, where the factor analysis method is used to determine initial values for estimating instrument noise and process disturbance variance. Because of the structural constraint of mass-balance equations, a gray-box estimation procedure must be adopted for which Bayesian network estimation via the expectation-maximization (EM) algorithm is a very suitable method. Therefore, this paper uses factor analysis to determine the initial values, and, afterward, estimates process and sensor variance by means of Bayesian estimation. After estimating the process and instrument variance, the process steady state and instrument bias can be similarly estimated.
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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 | 0.005 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".