Stochastic Data Envelopment Analysis: A Random Efficiency Perspective
Bibliographic record
Abstract
Since its inception, stochastic Data Envelopment Analysis (DEA) has found many applications. The approach commonly taken in stochastic DEA is via chance constraint models. This approach cannot, however, capture the inherent random fluctuations of the efficiency score caused by the random nature of the input and output variables. Having taken a random efficiency perspective, one can introduce an alternative approach that provides ground for capturing these fluctuations. One aspect of this alternative approach, which seems to have been neglected, concerns the distribution of the random efficiency score. We show that the efficiency score does not have a continuous distribution even if the random input and output variables distributions are continuous. The efficiency score distribution has, in fact, a point mass decomposition at 1. This observation renders the non-parametric bootstrap of efficiency score impossible. We introduce several criteria for the ranking and classification of Decision Making Units (DMUs) using a random efficiency perspective, including an interactive ranking method that incorporates managers’ knowledge and preferences. We then apply the point mass decomposition of efficiency score distributions of DMUs and show how these criteria can be implemented. We also discuss how one may estimate the efficiency score distributions of DMUs using both Bayesian and frequentist approaches. Our proposed methodology is illustrated using a real data set.
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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 | 0.006 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.010 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.005 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.006 |
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; both teacher heads agree on what is shown here.
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".