Markov Switching for Position Dependent Random Maps with Application to Forecasting
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Bibliographic record
Abstract
A Markov switching random map consists of a collection of transformations and a controlling stochastic matrix. In this process, at each time step, one transformation is selected randomly and applied. The selection of the transformations is controlled by the stochastic matrix of the process. In this note, we first prove the existence of absolutely continuous invariant measures (acims) for random maps, whose underlying transformations are piecewise monotonic, controlled by a position dependent stochastic matrix and study the ergodic properties of the acim. In particular, we prove a Birkhoff type ergodic theorem. Then we prove the existence of an acim for another class of Markov switching random maps based on geometric properties of the underlying transformations. We apply these results to forecasting in financial markets.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 it