The Half-Cycle Correction Explained: Two Alternative Pedagogical Approaches
Why this work is in the frame
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Bibliographic record
Abstract
Students of Markov decision models are often taught to add a half-cycle's worth of incremental utility to the cumulative total for each health state. The reason for this "half-cycle correction'' is often illustrated by a graph of the proportion of the hypothetical Markov cohort remaining in a given state. The ideal graph is shown as a smooth, declining, curve that represents the transition of patients randomly throughout each cycle. On the same graph, the effect of the accounting of state membership at the end of each cycle in discrete, computer-based approximations of the ideal Markov process is shown. Students are able to clearly see that the cumulative incremental utility in the discrete case underestimates the desired quantity. Likewise, they find the concept of shifting the ideal curve to the right by one-half cycle to reduce the latter discrepancy to be intuitive. However, students often find the approximate equivalence of shifting the ideal state membership curve and adding a half-cycle's worth of incremental utility to the total for the state at the beginning of a discrete Markov process to be a difficult cognitive leap. This article describes 2 pedagogical devices, algebraic and intuitive/visual approaches, that may assist the instructor of Markov theory to convey the latter concept. Elements of adult learning theory are discussed, which may help the instructor to choose which approach to employ. Implementation of the half-cycle correction in commonly used decision-analytic software is also discussed.
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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 | 0.017 | 0.023 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.002 |
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 it