[Question] Recovering latent probabilities from margin-distorted odds: de-vig model choice and pooling correlated estimators
Bookmaker odds (and prediction markets) imply probabilities that sum to more than 1 because of an embedded margin. I want the latent probabilities behind the distortion. A few things I can't resolve cleanly.
- Model choice for removing the margin. Proportional normalization, Shin (a latent proportion z of informed traders), and the power/log method impose different unobservable structures and give materially different estimates on short prices, enough to flip the sign of a downstream signal. Since you never observe the true p, only realized 0/1 outcomes and a later sharper price, is there a principled basis to discriminate between these models, or is it identifiability-limited and I should just report sensitivity across all three?
- Pooling under a missing low-bias reference. I anchor to one near-efficient source when available; when it's absent I take the median of the other sources' de-vigged probabilities. But those sources are strongly correlated (several are effectively clones), so the median behaves like a median of correlated estimators: it looks precise while carrying little independent information. How would you estimate an effective number of independent sources and down-weight accordingly, and is abstaining the more defensible choice when the low-bias anchor is gone?
- Combining a trusted low-variance estimator with a correlated ensemble. When the reference IS present, precision-weighting it against the consensus assuming independence is clearly wrong. Is there a clean correlation-aware pooling or shrinkage approach for one low-variance source plus many correlated higher-variance ones?
- Validation target. I grade earlier estimates against the closing price (a later, sharper estimate), not realized outcomes. Under a proper scoring rule, is "tracks the later estimator" a coherent target, or does it conflate calibration with just chasing a second estimate? And what does the selection bias look like when you only get a validation point on markets that reach a close?
(Aside that turned out to matter: my reference source silently dropped out of my data feed for months and the pipeline substituted the fallback the whole time while still labeling outputs "reference-anchored." The values populated fine, so nothing looked wrong. I only caught it after storing a per-observation flag for whether the reference actually contributed. Log provenance, not just values.)