Mathematics and statistics

Generalized linear mixed model

A generalized linear mixed model (GLMM) is a regression model that extends the generalized linear model with random effects, widely used in biostatistics, ecology, and agronomy.

Generalized linear model

A generalized linear model (GLM) is a regression framework linking exponential-family responses to predictors through a link function, formulated by Nelder and Wedderburn in 1972.

Generalized mean

The generalized mean, also called the power mean or Hölder mean, is a family of averaging functions parameterized by an exponent, including the arithmetic, geometric, and harmonic means.

Generalized method of moments

The generalized method of moments (GMM) is a statistical estimation method that estimates model parameters from moment conditions without a full likelihood, introduced by Lars Peter Hansen in 1982.

Generalized minimal residual method

The generalized minimal residual method (GMRES) is an iterative Krylov subspace method for solving large sparse nonsymmetric linear systems, proposed by Saad and Schultz in 1986.

Generalized Pareto distribution

The generalized Pareto distribution (GPD) is a two-parameter probability distribution describing the sizes of exceedances above a high threshold, the standard tool of peaks-over-threshold analysis in extreme value theory.

Generalized quadrangle

A generalized quadrangle is a point-line incidence structure containing no triangles but many ordinary quadrangles, introduced by Jacques Tits in 1959 to describe rank 2 groups of Lie type.

Generalized renewal process

The generalized renewal process (GRP), or g-renewal process, is a stochastic model for repairable systems where repairs restore an intermediate state via a virtual age function.

Generalized Riemann hypothesis

The generalized Riemann hypothesis (GRH) is an unproved conjecture stating that all nontrivial zeros of every Dirichlet L-function lie on the critical line where the real part is 1/2.

Generalized Stokes theorem

The generalized Stokes theorem, also called the Stokes-Cartan theorem, states that the integral of a form's exterior derivative over a manifold equals its integral over the boundary.

Generalized Verma module

The generalized Verma module, also called a parabolic Verma module, is a Lie algebra representation induced from a module over a parabolic subalgebra, generalizing the Verma module.

Generating function

A generating function, also called an ordinary generating function, is a power series whose coefficients encode a number sequence, so the whole sequence can be handled as one algebraic object.

Generating function transformation

A generating function transformation systematically converts one generating function, or the sequence of coefficients it encodes, into another, ranging from elementary operations to the binomial and Stirling transforms.

Generic structure

A generic structure, also called a Fraïssé limit or rich model, is a countable homogeneous structure containing every finite structure from a given class, unique up to isomorphism.

Genomic best linear unbiased prediction

Genomic best linear unbiased prediction (GBLUP) is a mixed-model method that estimates breeding values from dense SNP markers, replacing pedigree relationships with a genomic relationship matrix.

GenStat

GenStat is a commercial statistical software package for data analysis and graphics, developed at Rothamsted Experimental Station and now sold by VSN International, best known for its ANOVA and REML algorithms.

Gentzen's consistency proof

Gentzen's consistency proof, also known as Gentzen's theorem, is Gerhard Gentzen's 1936 proof that Peano arithmetic is consistent, using transfinite induction up to the ordinal ε0.

Genus (mathematics)

In mathematics, genus is a topological invariant that counts a surface's handles, so a sphere has genus 0 and a torus genus 1, with related versions in graph theory and knot theory.

Genus of a curve

The genus of a curve is a nonnegative integer measuring an algebraic curve's complexity; over the complex numbers it equals the number of handles of the curve as a Riemann surface.

GeoDa

GeoDa, short for Geographic Data Analysis, is a free, open-source desktop program for spatial data analysis developed by Luc Anselin at the University of Chicago.

Geodesic

A geodesic, or geodesic path, is a locally length-minimizing curve, the straightest possible path through curved space; in the plane geodesics are straight lines, on a sphere great circles.

Geodesic curvature

Geodesic curvature, written kg, is the curvature of a curve measured within the surface it lies on; a curve with zero geodesic curvature is a geodesic.

Geodesic flow

Geodesic flow is the dynamical system on a Riemannian manifold's tangent bundle that moves each tangent vector along the geodesic it determines at constant speed, modeling free-particle motion.

GeoGebra

GeoGebra is a free, open-source suite of interactive mathematics software combining geometry, algebra, and calculus, founded by Markus Hohenwarter in 2001 and used by over 100 million students.

Geographically weighted regression

Geographically weighted regression (GWR) is a local regression method, introduced by Brunsdon, Fotheringham, and Charlton in 1996, that fits separate coefficients at every location using distance-based weights.

Geoinformatics

Geoinformatics is the science and technology dealing with the structure, capture, storage, processing, and dissemination of spatial information, resting on Geographic Information Systems and remote sensing, with applications from urban planning to disaster response.