MODELING OF THE MAXIMUM ENTROPY PROBLEM AS AN OPTIMAL CONTROL PROBLEM AND ITS APPLICATION TO PDF ESTIMATION OF ELECTRICITY PRICE
Bibliographic record
Abstract
This paper proposes a novel two step modeling and analysis on the continuous random variable of electricity price. At the first step, the continuous optimal control theory is used to model and solve the maximum entropy problem for a continuous random variable. The maximum entropy principle provides a method to obtain least-biased Probability Density Function (pdf) estimation. In this paper, to find a closed form solution for the maximum entropy problem with any number of moment constraints, the entropy is considered as a functional measure and the moment constraints are considered as the state equations. Therefore, the pdf estimation problem can be reformulated as the optimal control problem. At the second step, the proposed unbiased pdf estimator is used to estimate the pdf of electricity price. Moreover, the statistical indices and the distributional characteristics of electricity price are analyzed at each load level. The simulation results on the electricity price data of New England, Ontario and Nord Pool electricity markets show the efficiency of the proposed pdf estimator. In addition, the obtained results show that by decreasing the load, the statistical and distributional characteristics of the electricity price inclined toward the statistical properties of the normal distribution.
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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 | 0.000 | 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 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".