Bayesian Paradigm and Optimal Nonlinear Filtering
Bibliographic record
Abstract
This chapter provides the general formulation of the optimal Bayesian filtering. Regarding the chosen criterion for optimality, different estimators are obtained including minimum mean-square error estimator, risk-sensitive estimator, maximum a posteriori estimator, minimax estimator, the most probable estimator, and maximum likelihood estimator. However, the Bayesian solution is a conceptual solution and must be approximated in many practical situations. Depending on the approximation method, different filtering algorithms are derived, which provide computationally tractable suboptimal Bayesian solutions. Fisher information provides a measure of the ability to estimate a quantity as well as a measure of the state of disorder in a system. In a related context, as a performance measure, the Cramér–Rao lower bound represents the lowest possible mean-square error in the estimation. An iterative procedure is presented for online computing of the posterior Cramér–Rao lower bound for Bayesian nonlinear filters based on the corresponding state-space models.
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 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 | 0.000 | 0.000 |
| 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 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.010 | 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 teacher head, 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".