Mathematics and statistics

Minkowski functional

The Minkowski functional, also called the gauge, assigns to each point the smallest scale at which it lands in a set, turning convex sets into seminorms.

Minkowski inequality

The Minkowski inequality, also called Minkowski's inequalities, is the triangle inequality for L^p spaces, stating ||f+g||p ≤ ||f||p + ||g||p for 1 ≤ p ≤ ∞.

Minkowski problem

The Minkowski problem, posed by Hermann Minkowski, asks which measures on the unit sphere occur as the surface area measure of a convex body in convex geometry.

Minkowski sum

The Minkowski sum of two sets is the set of all vector sums of their points, named for Hermann Minkowski, who used it in 1903 to study convex bodies.

Minkowski's theorem

Minkowski's theorem, or Minkowski's convex body theorem, is a geometry of numbers result stating that any sufficiently large convex body symmetric about the origin contains a lattice point.

Minor (linear algebra)

A minor in linear algebra is the determinant of a square submatrix formed by choosing certain rows and columns of a matrix, also called a minor determinant.

Mirror map (string theory)

In string theory and mirror symmetry, a mirror map is the change of variables identifying the parameter spaces of mirror Calabi–Yau geometries, built from Picard–Fuchs period solutions.

Missing at random

Missing at random (MAR) is a statistical assumption about incomplete data stating that missingness depends only on observed data, one of three mechanisms classified by Donald Rubin in 1976.

Missing data

Missing data, also called missingness or missing values, are values in a study or survey that went unrecorded, and are handled by imputation and weight adjustment.

Misuse of p-values

Misuse of p-values is the interpretation of p-values in ways their statistical meaning does not support, such as reading them as the probability that a hypothesis is true.

Misuse of statistics, also called abuse of statistics, is the misleading use, presentation, or interpretation of statistical data through deliberate spin, careless error, or misunderstanding, arising in research, journalism, advertising, and politics.

Mittag-Leffler function

The Mittag-Leffler function is an entire function defined by a power series with gamma-function coefficients, introduced by Gösta Mittag-Leffler in 1903 and reducing to the exponential at α = 1.

Mixed data sampling regression

Mixed data sampling (MIDAS) regression is an econometric method that regresses a low-frequency variable, such as quarterly GDP growth, on more frequently sampled predictors, like monthly indicators, using parsimonious distributed lag weights.

Mixed design (statistics)

A mixed design is an experimental design combining a between-groups factor with a within-subjects repeated-measures factor, also called a split-plot design and commonly used in pretest-posttest studies.

Mixed finite element method

A mixed finite element method is a Galerkin technique approximating two or more coupled fields of a partial differential equation at once, such as velocity and pressure.

Mixed logit

Mixed logit, also called the mixed logit model, is a discrete choice model in which utility coefficients vary randomly over decision makers, relaxing the limits of standard logit.

Mixed model

A mixed model is a statistical model combining fixed effects, constant across the population, with random effects attached to units, used for clustered and longitudinal data.

Mixed radix

Mixed radix, also called mixed base, is a positional numeral system in which each digit position has its own radix, unlike the single fixed base of decimal.

Mixed volume

Mixed volume is a multilinear extension of volume to convex bodies, defined as a coefficient of the volume polynomial; it is central to convex geometry.

Mixed-integer optimization

Mixed-integer optimization is a family of mathematical optimization methods for problems combining continuous variables with integer or discrete values, solved by branch-and-bound and cutting planes over relaxations.

Mixed-integer quadratic programming

Mixed-integer quadratic programming (MIQP) is an optimization method that minimizes a quadratic objective subject to linear constraints, where some variables must take integer values and others stay continuous.

Mixing (mathematics)

Mixing is a property of measure-preserving dynamical systems in which past and future events become statistically independent over time, one level of the ergodic hierarchy.

Mixing time of Markov chains

The mixing time of a Markov chain is the number of steps needed for its distribution to become close to its stationary distribution, regardless of the starting state.

Mixture design

A mixture design is a design of experiments in which the factors are the proportions of components in a blend, constrained to be non-negative and to sum to one.

Mixture distribution

A mixture distribution is a probability distribution formed as a weighted combination of component distributions, equivalent to choosing a component at random and then sampling from it.

Mixture model

A mixture model is a probability model in which data are assumed to come from several component distributions, weighted so the weights sum to one.

Mixture regression (statistics)

Mixture regression is a statistical modeling method that fits a weighted combination of regression models, identifying latent subpopulations with different predictor–outcome relationships from unlabeled data.

Möbius function

The Möbius function, μ(n), is an arithmetic function taking values −1, 0, and 1: (−1)^k for products of k distinct primes, and 0 on non-squarefree integers.

Möbius inversion formula

The Möbius inversion formula, also called Möbius inversion, is a number theory theorem stating that if f(n) is the divisor sum of g(n), then g is recovered using the Möbius function.