Mathematics and statistics

Steiner system

A Steiner system S(t, k, v) is a combinatorial design in which v points and k-element blocks cover every set of t points exactly once.

Steiner tree problem

The Steiner tree problem, named after Swiss mathematician Jakob Steiner, asks for a minimum-cost tree connecting terminals in a graph or geometric space, and is NP-hard.

Steiner triple system

A Steiner triple system of order n is a set of n points whose triples cover every pair exactly once, existing only when n is 1 or 3 mod 6.

Stem-and-leaf display

A stem-and-leaf display, also called a stemplot, is a data display that splits each value into a stem and a leaf, showing distribution shape while keeping all values.

Step detection

Step detection is a signal processing and statistical method that locates abrupt steps in a noisy time series, estimating when the signal jumps and each segment's level.

Step function

A step function, also called a staircase function, is a real-valued function that is constant on finitely many pieces of its domain, as in the Heaviside step function.

Stepwise regression

Stepwise regression is a family of automated variable-selection methods for regression in which predictors are added or removed one at a time by significance tests or information criteria.

Stereographic projection

Stereographic projection is a way of mapping a sphere onto a plane by projecting from a pole; it preserves angles and maps circles to circles or lines.

Stereology is a set of mathematical sampling methods that estimate three-dimensional properties of solid materials and tissues, such as volume, surface area, and cell number, from two-dimensional microscopic sections.

Stiefel manifold

The Stiefel manifold is the space of all orthonormal k-frames, or ordered sets of mutually orthogonal unit vectors, in n-dimensional space, a compact manifold named after Eduard Stiefel.

Stieltjes transform

The Stieltjes transform of a measure μ on the real line is sμ(z) = ∫ μ(dx)/(x − z), an analytic function that encodes the measure.

Stigler's law of eponymy

Stigler's law of eponymy is the proposition that no scientific discovery is named after its original discoverer, set out by statistician Stephen Stigler in 1980 and credited to Robert Merton.

Stirling numbers

Stirling numbers are two families of integer arrays, s(n, k) and S(n, k), counting permutations of a set by cycles and partitions into nonempty subsets, named for James Stirling.

Stirling numbers and exponential generating functions in symbolic combinatorics

Stirling numbers of the first and second kind have closed-form exponential generating functions, which in symbolic combinatorics turn classical recurrences into consequences of simple set constructions.

Stirling numbers of the first kind

Stirling numbers of the first kind, named for James Stirling, count the permutations of n objects that decompose into exactly k cycles and appear as coefficients when a falling factorial is expanded in powers.

Stirling numbers of the second kind

Stirling numbers of the second kind, also called Stirling partition numbers, count the ways to partition a set of n labeled elements into exactly k nonempty subsets.

Stirling's approximation

Stirling's approximation, also called Stirling's formula, is the asymptotic formula n! ≈ √(2πn)(n/e)^n for large n, published by James Stirling in Methodus differentialis in 1730, with relative error about 1/(12n).

STIRPAT model

The STIRPAT model, a stochastic reformulation of the IPAT identity, is a regression framework estimating how population, affluence, and technology drive environmental impacts such as CO2 emissions.

Stochastic

Stochastic, or stochasticity, describes systems and models that involve randomness, so the same starting conditions can produce different results; the central object is the stochastic process.

Stochastic actor-oriented model

The stochastic actor-oriented model (SAOM) is a statistical model for longitudinal social network data, treating network change as the accumulated choices of individual actors; it is fitted with the R package RSiena.

Stochastic approximation

Stochastic approximation is a family of iterative algorithms that find the root of an unknown function from noisy observations, introduced by Robbins and Monro in 1951.

Stochastic block model

The stochastic block model, introduced by Holland, Laskey, and Leinhardt in 1983, is a statistical model for networks in which edge probabilities depend only on nodes' blocks.

Stochastic calculus

Stochastic calculus, also known as stochastic analysis or stochastic integration, extends calculus to random processes like Brownian motion, using the Itô integral and Itô's formula.

Stochastic control

Stochastic control is the branch of control theory and applied probability that finds optimal decision rules for random dynamical systems, minimizing expected cost or maximizing reward.

Stochastic differential equation

A stochastic differential equation (SDE) is a differential equation containing a stochastic process, typically a drift term plus noise driven by Brownian motion, used in finance, biology, and physics.

Stochastic dominance

Stochastic dominance is a statistical method for ranking risky prospects by comparing their cumulative distribution functions, without assuming a specific utility function; first-order dominance requires only increasing preferences.

Stochastic filtering

Stochastic filtering is a class of methods in probability and signal processing that estimate the hidden state of a dynamical system from noisy observations, updating the estimate recursively.

Stochastic frontier model

The stochastic frontier model is an econometric regression model proposed in 1977 that estimates production or cost frontiers, separating random statistical noise from technical inefficiency.

Stochastic heat equation

The stochastic heat equation is a stochastic partial differential equation adding random noise to the classical heat equation; it is a prototypical SPDE studied across dimensions.