6,052 articles
Gammoid
A gammoid is a matroid defined from a directed graph: a vertex set whose independent subsets are those reachable by vertex-disjoint paths from a starting set.
GAP (computer algebra system)
GAP (Groups, Algorithms and Programming) is a free, open-source, extensible system for computation in discrete abstract algebra, emphasizing computational group theory and used in research and teaching.
Gap test (randomness testing)
The gap test is a chi-square goodness-of-fit test checking whether spacings between recurrences of a chosen value in a random number sequence follow the expected geometric distribution.
GARCH model
The GARCH model, generalized from Engle's ARCH by Bollerslev in 1986, forecasts the conditional variance of returns from past squared errors, and its GARCH(1,1) form is the workhorse volatility model for daily returns.
Garden of forking paths
The garden of forking paths is a 2013 statistical concept by Andrew Gelman and Eric Loken describing how data-dependent analysis choices create a multiple comparisons problem without conscious p-hacking.
Garfield's proof of the Pythagorean theorem
Garfield's proof of the Pythagorean theorem is a geometric proof devised in 1876 by James A. Garfield, then a US congressman and later the 20th president.
Gauss map
The Gauss map of an oriented surface in 3D space assigns to each point its unit normal vector on the unit sphere; its differential encodes the surface's curvature.
Gauss sum
A Gauss sum, or Gaussian sum, is a finite sum pairing a multiplicative character with an additive character, studied by Carl Friedrich Gauss in 1801.
Gauss–Bonnet theorem
The Gauss–Bonnet theorem is a differential geometry result stating that a compact orientable surface's total Gaussian curvature equals 2π times its Euler characteristic, connecting local curvature with global topology.
Gauss–Newton algorithm
The Gauss–Newton algorithm, or Gauss–Newton method, is an iterative method for minimizing nonlinear least squares problems, solving a linear least squares step each iteration without second derivatives.
Gauss–Seidel method
The Gauss–Seidel method is an iterative method for solving linear systems, a refinement of the Jacobi method described by Ludwig Seidel in 1874 and named for him and Carl Friedrich Gauss.
Gaussian approximation (density evolution)
The Gaussian approximation is a one-dimensional simplification of density evolution, assuming decoder messages follow Gaussian distributions; introduced for LDPC codes by Chung, Richardson, and Urbanke in 2001.
Gaussian binomial coefficient
The Gaussian binomial coefficient, or q-binomial coefficient, is a polynomial in q that counts the k-dimensional subspaces of an n-dimensional vector space over a finite field of q elements.
Gaussian copula
The Gaussian copula is a probability model that couples random variables by multivariate normal dependence while their margins stay arbitrary; it was widely used to price structured credit before the 2008 financial crisis.
Gaussian curvature
Gaussian curvature is the product of the two principal curvatures of a surface at a point. Gauss introduced it in 1827, proving it is measurable from within the surface.
Gaussian elimination
Gaussian elimination, also known as row reduction, is an algorithm that solves systems of linear equations by reducing a matrix to upper triangular form and applying back substitution.
Gaussian free field
The Gaussian free field is a centered Gaussian random field with covariance given by the Laplacian's Green function, described as a higher-dimensional analog of Brownian motion.
Gaussian function
The Gaussian function, also known as the Gaussian curve, is a function whose graph is a symmetric bell-shaped curve that falls off rapidly, named after Carl Friedrich Gauss.
Gaussian graphical model
A Gaussian graphical model, or covariance selection model, is a probabilistic graphical model for Gaussian variables whose graph edges correspond to nonzero entries of the inverse covariance matrix.
Gaussian integer
A Gaussian integer, also known as a complex integer, is a complex number a + bi where a and b are ordinary integers, named for Carl Friedrich Gauss.
Gaussian integral
The Gaussian integral, also known as the Euler-Poisson integral, is the integral of the Gaussian function over the whole real line, equal to the square root of pi.
Gaussian isoperimetric inequality
The Gaussian isoperimetric inequality, proven independently by Sudakov and Tsirelson and by Borell in the 1970s, states that half-spaces minimize Gaussian perimeter among sets of given measure, implying Gaussian concentration.
Gaussian Markov process
A Gaussian Markov process is a stochastic process that is both Gaussian and Markov, so its future depends only on its present value; examples include Brownian motion and the Ornstein–Uhlenbeck process.
Gaussian measure
A Gaussian measure is a probability measure on an infinite-dimensional space, such as a Banach or Hilbert space, where every continuous linear functional is a Gaussian random variable.
Gaussian mixture model
A Gaussian mixture model is a probabilistic model representing data as a weighted sum of Gaussian distributions, used for soft clustering and fitted with the EM algorithm.
Gaussian orthogonal ensemble
The Gaussian orthogonal ensemble (GOE) is a probability distribution on real symmetric matrices whose law is invariant under conjugation by orthogonal matrices, introduced by Eugene Wigner for nuclear level statistics.
Gaussian prime
A Gaussian prime is a Gaussian integer like 1 + i or 3 that cannot be factored except by units, classified by Carl Friedrich Gauss in 1832.
Gaussian process
A Gaussian process, also called a Gaussian stochastic process, is a stochastic process where every finite subset of variables has a joint multivariate Gaussian distribution.
Gaussian process regression
Gaussian process regression, developed in geostatistics as kriging, is a Bayesian method that places a Gaussian process prior over functions and predicts with calibrated uncertainty.
Gaussian random field
A Gaussian random field is a collection of random variables over space where every finite set follows a normal distribution, the standard model of spatial uncertainty.