Statistical Inference & Hypothesis Testing

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Abstractions about drawing conclusions from data through likelihood-based estimation, Bayesian posterior reasoning, hypothesis tests, error measures and generalization biases, spanning parametric, nonparametric and sequential inference methods.

34 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.

• Bayesian linear regression — A linear conditional model that combines a likelihood for outcomes with prior distributions over coefficients and noise parameters to obtain posterior inference and prediction.
• Bayesian model reduction — A method deriving evidence and posterior parameters for models with altered priors from a previously fitted full Bayesian model.
• Brown–Forsythe test — A robust test of equality of group variances obtained by applying one-way ANOVA to absolute deviations from group medians.
• Deviance (statistics) — A likelihood-based goodness-of-fit quantity comparing a fitted statistical model with a saturated model, conventionally twice their maximized log-likelihood difference.
• Duck test — A colloquial abductive heuristic that identifies an unknown by the convergence of several familiar, repeatedly observed characteristics.
• Empirical likelihood — A nonparametric likelihood method that assigns probabilities to observed sample points and maximizes their product subject to estimating-equation constraints.
• Empirical probability — An event-probability estimate given by its observed relative frequency in a finite sample of trials.
• Exact test — A hypothesis test whose null distribution and resulting type-I error control are derived without an asymptotic approximation under the stated sampling model.
• Faulty generalization — An informal fallacy that infers a broad population claim from evidence too small, biased or unrepresentative to warrant that scope.
• Generalized p-value — A nuisance-parameter-controlled tail probability derived from a generalized pivotal quantity for testing hypotheses lacking a conventional exact pivot.
• Information field theory — A Bayesian statistical field theory for reconstructing continuous fields from incomplete noisy data using field priors and methods adapted from quantum field theory.
• Likelihood principle — The proposition that, for a fixed statistical model, all sample evidence about its parameters is contained in the observed-data likelihood up to proportionality.
• MAGIC criteria — A five-part framework for evaluating whether a statistical argument is compelling through magnitude, articulation, generality, interestingness and credibility.
• Marginal likelihood — The probability density of observed data under a Bayesian model after integrating the likelihood over the prior distribution of its parameters.
• Maximum likelihood estimation — Parameter estimation by selecting the model value that makes the observed data most likely under a specified statistical family.
• Mean absolute error — The arithmetic mean of absolute differences between paired predictions or estimates and corresponding observed or reference values.
• Normal-inverse-gamma distribution — A four-parameter joint distribution in which a variance has an inverse-gamma law and a mean conditional on that variance is normal, conjugate for a normal model with unknown mean and variance.
• Normality test — A statistical diagnostic or hypothesis test assessing whether observed data are compatible with a normal-distribution model.
• Nuisance parameter — A model parameter not itself of inferential interest but necessary to account for when estimating or testing the target parameter.
• Observed information — The negative Hessian of a sample log-likelihood evaluated at a specified parameter value, measuring local realized curvature.
• Oversampling and undersampling in data analysis — Resampling strategies that alter class frequencies in a dataset by adding or repeating minority observations or removing majority observations.
• Paired difference test — A statistical location test applied to within-pair differences when two measurements are linked by subject, unit, match, or repeated observation.
• Pivotal quantity — A function of observed data and unknown model parameters whose sampling distribution is independent of every unknown parameter.
• Posterior probability — The probability distribution for an uncertain hypothesis or parameter after combining a prior distribution with observed-data likelihood through Bayes' rule.
• Principle of marginality — The modeling principle that an interaction term should ordinarily be accompanied by its constituent lower-order main effects, whose meanings are marginal across the interacting variable.
• Score test — A likelihood-based hypothesis test using the score gradient and information matrix evaluated at the null-constrained parameter estimate.
• Sequential analysis — Statistical inference in which data are evaluated as they arrive and sampling stops according to a predeclared evidence rule rather than a fixed sample size.
• Standard error — The standard deviation of a statistic's sampling distribution, quantifying how much the statistic would vary across repeated samples under the stated design and model.
• Sunrise problem — The problem of assigning predictive probability to the next recurrence of a repeatedly observed event, exposing how induction depends on prior assumptions.
• T-statistic — A standardized statistic equal to an estimate’s departure from a hypothesized value divided by its estimated standard error.
• Testing hypotheses suggested by the data — The invalid reuse of the same observations both to select a hypothesis and to test it as though the test had been specified independently.
• Wald test — A hypothesis test comparing an unrestricted parameter estimate with a constrained null value using its estimated covariance as a precision weight.
• Widely applicable information criterion — A Bayesian predictive-fit criterion combining log pointwise posterior predictive density with a variance-based effective-complexity penalty.
• Will Rogers phenomenon — The rise of both group averages when observations between the two original means are reclassified from the higher-mean group to the lower-mean group.