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Statistical Bias & Inference Pitfalls

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Abstractions that diagnose bias and paradox in statistical estimation and decision-making, covering estimation pitfalls (endogeneity, Stein's paradox, ecological inference problem), fairness and imbalance issues in classification (class imbalance, equalized odds), and a descriptive risk model, cumulative prospect theory.

7 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

  • Class Imbalance — Diagnose why a 99%-accurate classifier can be useless: when one class vastly outnumbers the class of interest, additive loss aggregation lets majority examples dominate the gradient, so the model learns to ignore the rare minority.
  • Cumulative Prospect Theory — A descriptive model that values gains and losses from a reference point and applies rank-dependent decision weights to cumulative probabilities before aggregating a risky prospect.
  • Ecological Inference Problem — Recover individual-level joint distributions from group-level marginal totals, a many-to-one inverse problem where the data alone only pin the answer to the Duncan-Davis bounds and any tighter estimate rests on an explicit, contestable identifying assumption.
  • Endogeneity — The condition in which a regressor is correlated with a model's error term — through confounding, simultaneity, or measurement error — so OLS coefficients are biased and inconsistent for the causal effect, collapsing the coefficient's causal reading while leaving its predictive one intact.
  • Equalized odds — A classifier fairness criterion requiring protected groups to have equal true-positive and false-positive rates conditional on the actual outcome.
  • Fractional Response Model — A fractional response model estimates how covariates change the conditional mean of a proportion in [0,1] through a bounded link, retaining exact zero and one observations.
  • Stein's Paradox — The result that estimating three or more means each by its own sample mean is inadmissible under total squared-error loss — a shrinkage estimator pulling each toward a common reference achieves strictly lower joint error for every true parameter vector, however unrelated the quantities.