Statistical Inference & Uncertainty

Primes about reasoning from noisy samples to general conclusions while quantifying doubt: inference machinery (hypothesis testing, confidence intervals, statistical power, p-values), pitfalls that distort conclusions (overfitting, regression to the mean, multiple comparisons), and the underlying assumptions and methods (distributional assumptions, nonparametric methods, randomization, inductive reasoning).

18 primes in this family — primes that sit near one another in abstraction space (k-means over structural-signature embeddings). Each is shown with its short description.

• Bayesian Cue Integration — Multiple noisy cues to one quantity combine by inverse-variance weighting into a lower-variance estimate.
• Causal reasoning — Infer, compare, test, or revise cause–effect structure by distinguishing interventions and counterfactual alternatives from association alone.
• Confidence Intervals — Range of plausible values.
• Distributional Assumption — Commitment to assume uncertain quantities follow specific distribution.
• Estimation — Derive a usable value, range or state for an unknown quantity from incomplete, noisy or indirect information, with assumptions, uncertainty and decision purpose made explicit.
• Hypothesis Testing (Null vs. Alternative) — Null vs alternative evaluation.
• Inductive Reasoning — Specific to general inference.
• Multiple Comparisons Correction — Adjust the thresholds or p-values of a defined family of simultaneous tests so a chosen family-level error criterion remains bounded despite multiplicity.
• Nonparametric Methods — Distribution-free analysis.
• Overfitting — Poor generalization.
• Randomization — Assign by chance.
• Regression to the Mean — Extremes return toward average.
• Statistical Inference — Reasoning from a finite, noisy sample back to the underlying population or process while explicitly quantifying the uncertainty that sampling introduces.
• Statistical Power — Probability of detecting effect.
• Statistical Significance (p-Value) — Likelihood results are random.
• Statistical syllogism — Project a qualified proportion from a declared reference class onto a particular member as defeasible support for that member's having the attribute, with inferential strength inherited from the proportion and revised when a more relevant class or case-specific fact becomes available.
• Type I & Type II Errors — False positive/negative.
• Uncertainty — Incomplete knowledge.