Mathematics and statistics

Score test

The score test, known in econometrics as the Lagrange multiplier test, is a statistical hypothesis test introduced by C. R. Rao in 1948 that requires fitting only the restricted model.

Scoring rule

A scoring rule is a function assigning a numerical score to a probabilistic forecast and the observed outcome, used to compare forecasters; a proper rule rewards stating one's true beliefs.

Screening design

A screening design is a statistical experimental plan that identifies the few significant factors among many candidates, emphasizing main effects, and typically opens a sequence of experiments.

Seasonal adjustment

Seasonal adjustment is a statistical procedure that removes recurring seasonal and calendar effects from a time series, standard practice for monthly and quarterly official statistics.

The seasonal ARIMA (SARIMA) model is a univariate time-series forecasting method that extends ARIMA with seasonal autoregressive, differencing, and moving-average terms, capturing periodic patterns like annual cycles in monthly data.

Seasonal-trend decomposition

Seasonal-trend decomposition (STL) is a statistical procedure that splits a seasonal time series into trend, seasonal, and remainder components, introduced by Cleveland and colleagues in 1990.

Secant line

A secant line is a straight line that cuts a curve at two or more points. Its slope gives the average rate of change, and its limit is the tangent line.

Secant method

The secant method is an iterative numerical algorithm for finding a root of a function using two starting values and no derivative, converging at rate about 1.618.

Second derivative

The second derivative, or second-order derivative, written f''(x), is the derivative of a function's derivative, measuring how the rate of change itself changes, as with acceleration.

Second fundamental form

The second fundamental form, or second fundamental tensor, is a bilinear form measuring how a surface bends within the space that contains it, introduced by Gauss in 1827.

Second moment method

The second moment method is a technique in probability and combinatorics that shows a nonnegative random variable is positive or near its mean by controlling its variance, using Chebyshev's inequality.

Second variation

The second variation is the second-order term in the expansion of a functional under small perturbation, playing the role of the second derivative test in the calculus of variations.

Second-countable space

A second-countable space, or second axiom of countability, is a topological space with a countable base: every open set is a union of countably many basic open sets.

Second-order arithmetic

Second-order arithmetic, also called second-order Peano arithmetic, is a formal axiomatic system over natural numbers and sets of them, stronger than Peano arithmetic, weaker than set theory, and the standard framework for reverse mathematics.

Second-order cone programming

Second-order cone programming (SOCP) is a convex optimization method minimizing a linear function subject to Euclidean-norm constraints, used in portfolio optimization, engineering design, and machine learning.

Second-order logic

Second-order logic is a formal logical system whose quantifiers range over properties, relations, and functions, not just individuals; unlike first-order logic, it can uniquely characterize structures like the natural numbers.

Secondary data

Secondary data is data collected by a party other than the researcher who later analyzes it, including census data, government administrative records, geospatial data, and datasets archived from earlier studies.

Secretary problem

The secretary problem, also known as the Sultan's Dowry Problem, is an optimal stopping problem in which candidates are seen one at a time in random order.

Sectional curvature

Sectional curvature is a number assigned to each tangent 2-plane of a Riemannian manifold, measuring Gaussian curvature; the curvatures of all planes determine the Riemann tensor.

Sedenion

A sedenion is a 16-dimensional hypercomplex number, the fifth algebra in the Cayley–Dickson sequence after the octonions: non-associative and non-alternative, but power-associative, and the first to contain zero divisors.

Sedenions

Sedenions are 16-dimensional noncommutative, nonassociative algebras over the real numbers, obtained by applying the Cayley-Dickson construction to the octonions; unlike the octonions, they contain zero divisors.

Seemingly unrelated regressions

Seemingly unrelated regressions (SUR), also called SURE or Zellner estimation, is a statistical method for jointly estimating several regression equations whose errors are correlated across equations.

Segmented regression

Segmented regression is a statistical method that fits piecewise linear relationships between a predictor and an outcome, estimating breakpoint locations and slopes, widely used in interrupted time series analysis.

Seiberg–Witten invariants

Seiberg–Witten invariants are diffeomorphism invariants of smooth closed four-manifolds, introduced in 1994 by Nathan Seiberg and Edward Witten, who derived the defining equations from supersymmetric Yang–Mills theory.

Selberg trace formula

The Selberg trace formula is an identity in harmonic analysis, introduced by Atle Selberg in 1956, that equates a sum over Laplace eigenvalues with a sum over closed geodesics.

Selection bias

Selection bias, also known as selection effect, is a distortion in an estimated association arising when the choice of which observations enter a study relates to both exposure and outcome.

Selective inference

Selective inference is a statistical framework for p-values and confidence intervals that stay valid when the hypothesis or model tested was chosen from the same data used to test it.

Selectivity ratio

The selectivity ratio (SR) is a variable-importance measure in partial least squares regression that ranks predictors by explained over residual variance, introduced by Rajalahti and colleagues in 2008.

Self-reference

Self-reference, also called self-reflexivity, is the relation an object bears when it refers to itself, the source of the liar paradox and Gödel's incompleteness theorems.