Mathematics and statistics

Neighbourhood (mathematics)

A neighborhood of a point in a topological space is a set containing the point in its interior, formalizing local closeness without any notion of distance.

Néron model

The Néron model, or Néron minimal model, is a smooth group scheme extending an abelian variety so every rational point extends, introduced by André Néron in 1964.

Nest algebra

A nest algebra is the algebra of bounded operators on a Hilbert space leaving invariant every subspace in a nest, a totally ordered collection of closed subspaces.

Nested cross-validation, also called double cross-validation, runs an inner tuning loop within each outer cross-validation fold, avoiding the optimistic bias of scoring a model on data used to tune it.

Nested intervals

Nested intervals are intervals of the real line, each containing the next; the nested interval property says closed, bounded nested intervals share a common point.

Nested logit model

The nested logit model is a discrete choice model grouping alternatives into nests so unobserved utilities may correlate within a group, relaxing the multinomial logit's IIA assumption.

Nested sampling

Nested sampling is a Monte Carlo algorithm in Bayesian statistics, introduced by John Skilling in 2006, that computes a model's evidence with posterior samples as a by-product.

Net (mathematics)

A net, also called a Moore–Smith sequence, is a function from a directed set into a topological space, generalizing sequences so convergence describes limits and compactness in every topology.

Network

A network is a set of nodes connected by edges, the same structure mathematicians call a graph, used to model social relationships, the Internet, power grids, and transportation.

Network data envelopment analysis

Network data envelopment analysis (NDEA) is a nonparametric linear-programming method in operations research that measures efficiency of units split into connected sub-processes, locating where inefficiency arises.

Network matrix

A network matrix is a {0, +1, −1}-matrix built from a directed tree and graph: each entry records how a tree path traverses an arc, and it is totally unimodular.

Network meta-analysis

Network meta-analysis, also called mixed treatment comparisons, is a statistical method comparing three or more treatments in one analysis, combining direct and indirect trial evidence.

Network meta-regression

Network meta-regression (NMR) is a statistical method in evidence synthesis that extends network meta-analysis by adding study-level covariates. It estimates interactions to see if effect modification explains heterogeneity.

Network sampling

Network sampling is a family of survey methods for drawing samples of hard-to-reach, hidden populations by following links of an underlying social network instead of a complete list.

Network theory

Network theory studies systems of interconnected entities as nodes and edges, with two main strands: social network analysis and network science, both rooted in graph theory.

Network tomography

Network tomography is a statistical method, introduced by Y. Vardi in 1996, that infers internal link delay, loss, or traffic from end-to-end measurements between edge nodes.

Neumann problem

The Neumann problem, also called the second boundary value problem, is a partial differential equation problem that prescribes the normal derivative, not the value, on the boundary.

Neumann series

The Neumann series is the infinite series of powers of a bounded linear operator, the operator analog of the geometric series, named after Carl Gottfried Neumann.

Neural posterior estimation

Neural posterior estimation (NPE) is a simulation-based Bayesian method that trains a neural density estimator on simulated parameter–data pairs to approximate posteriors without a likelihood function.

Neuro-fuzzy

Neuro-fuzzy, also called a fuzzy neural network, is a hybrid intelligent system combining neural networks with fuzzy logic, whose landmark model is ANFIS from 1993.

Nevanlinna theory

Nevanlinna theory, created by Rolf Nevanlinna in the 1920s, quantifies how often and how closely meromorphic functions take each value, refining Picard's and Borel's theorems.

New Foundations

New Foundations, also called typed set theory, is an axiomatic set theory proposed by W. V. Quine in 1937, known for admitting a universal set.

Newsvendor model

The newsvendor model, also called the newsboy problem, is a single-period inventory model that finds the profit-maximizing order quantity for a product with uncertain demand and no chance to reorder.

Newton interpolation

Newton interpolation is a numerical analysis method, attributed to Isaac Newton, for constructing the polynomial that passes through given data points, with coefficients given by the data's divided differences.

Newton polytope

A Newton polytope is the convex hull of the exponent vectors of a polynomial's terms, converting questions about sparse polynomials into questions of convex geometry.

Newton's identities

Newton's identities, also called the Newton–Girard identities, are relations expressing the power sums of variables in terms of elementary symmetric polynomials, first published by Newton in 1707.

Newton's method

Newton's method, also known as the Newton-Raphson method, is an iterative algorithm for solving f(x) = 0: each step replaces the estimate with the x-intercept of the tangent line.

Neyman allocation

Neyman allocation is a stratified sampling rule that assigns each stratum a sample size proportional to its population size and standard deviation, minimizing variance at fixed total sample size.

Neyman–Pearson lemma

The Neyman–Pearson lemma is a theorem in mathematical statistics stating that, for testing a simple null against a simple alternative, the likelihood ratio test is most powerful.