Mathematics and statistics

Skein relation

A skein relation is a linear relation among link diagrams identical except at one crossing site, which defines and computes polynomial invariants of knots and links.

Skew lines

Skew lines are two straight lines in three-dimensional space that do not intersect and are not parallel; a standard example is two nonparallel edges of a cube.

The skew normal distribution, or skewed gaussian, is a family of continuous probability distributions introduced by Adelchi Azzalini in 1985 that extends the normal distribution with an asymmetry shape parameter.

Skew polynomial ring

A skew polynomial ring, also called an Ore extension, is a noncommutative polynomial ring in which the variable does not commute with coefficients, introduced by Øystein Ore in 1933.

Skew-symmetric matrix

A skew-symmetric matrix, also known as an antisymmetric matrix, is a square matrix equal to the negative of its transpose, so its diagonal entries are zero.

Skewness

Skewness is a measure of the asymmetry of a probability distribution or data set, most commonly computed as the standardized third central moment, with zero indicating symmetry.

Skolem normal form

Skolem normal form, also known as Skolem standard form, is a form of a first-order logic formula with only universal quantifiers, introduced by Thoralf Skolem in 1920.

Skolemization

Skolemization is a transformation in first-order logic that removes existential quantifiers by replacing their variables with newly introduced Skolem functions, producing a formula satisfiable if and only if the original.

Skorokhod integral

The Skorokhod integral, also called the Hitsuda–Skorokhod integral, is a stochastic integral extending the Itô integral to non-adapted integrands, introduced by A. V. Skorokhod in 1975.

Slice sampling

Slice sampling is a Markov chain Monte Carlo method introduced by Radford M. Neal in 2003 that samples from a density by uniformly sampling the region under its curve.

Sliced inverse regression

Sliced inverse regression (SIR) is a statistical dimension reduction method that finds linear combinations of predictors carrying a response's information, introduced by Ker-Chau Li in 1991.

Slope

Slope of a line, also called the gradient, is the ratio of vertical change (rise) to horizontal change (run); horizontal lines have slope 0, vertical lines undefined slope.

Small area estimation

Small area estimation (SAE) is a collection of statistical methods that produce model-based estimates for small geographic areas by combining survey data with auxiliary information.

Small-angle approximation

The small-angle approximation, or small-angle formula, replaces sin θ and tan θ with θ for small angles in radians, turning trigonometric equations into linear ones.

Smith normal form

The Smith normal form is a canonical diagonal form of a matrix over a principal ideal domain, introduced by Henry John Stephen Smith in 1861.

Smoluchowski coagulation equation

The Smoluchowski coagulation equation, introduced by Marian Smoluchowski in 1916, is an integrodifferential equation describing how pairs of particles or clusters merge irreversibly into larger ones.

Smoothing problem (stochastic processes)

The smoothing problem in stochastic processes estimates a system's state using observations from both before and after that time, giving more accurate estimates than filtering at the cost of extra computation.

Smoothing spline

A smoothing spline is a nonparametric regression method that fits a flexible curve to data by minimizing squared errors plus a roughness penalty, with a smoothing parameter controlling wiggliness.

Smoothness

Smoothness is the property of functions and maps having derivatives of all orders that vary continuously, called C-infinity, in contrast to Ck functions with only k continuous derivatives.

Snort (game)

Snort is a two-player graph-coloring game attributed to Simon Norton, in which adjacent vertices may not differ in color and a player with no move loses.

Snowball sampling

Snowball sampling, also called respondent-driven sampling, is a non-probability sampling method in which existing participants recruit acquaintances, mainly used to reach hidden or hard-to-reach populations.

Sobel test

The Sobel test is a large-sample z-test of whether the indirect effect a·b in a mediation model differs from zero, introduced by Michael E. Sobel in 1982.

Sobol sensitivity analysis

Sobol sensitivity analysis is a variance-based method of global sensitivity analysis, introduced by I. M. Sobol' in 1990, that measures how much each input of a model contributes to output variance.

Sobolev inequality

The Sobolev inequality is a functional inequality in analysis, proved by Sergei Sobolev in 1938, bounding a function's L^q norm by the L^p norm of its gradient.

Sobolev space

A Sobolev space is a vector space of functions whose weak derivatives up to a given order lie in an L^p space, introduced by Sergei Sobolev in the 1930s.

Social spider optimization

Social spider optimization (SSO) is a population-based metaheuristic algorithm, introduced by Erik Cuevas and colleagues in 2013, that models social spiders to solve numerical optimization problems.

Society of Actuaries

The Society of Actuaries is a Chicago-based professional body, formed in 1949, that credentials and educates actuaries in life insurance, health, retirement, and enterprise risk management.

Socio-Economic Panel

The Socio-Economic Panel (SOEP; German: Sozio-oekonomisches Panel) is a German household survey that has interviewed people annually since 1984, tracking income, employment, education, and health.

Softmax function

The softmax function, also known as the normalized exponential, converts a vector of scores into probabilities that sum to 1; it is the standard output layer of multi-class neural classifiers.