Mathematics and statistics

Multinomial probit

Multinomial probit is a discrete-choice regression model estimating probabilities of choosing among unordered categories, with multivariate normal errors that relax the IIA restriction of multinomial logit.

Multinomial theorem

The multinomial theorem, also called the multinomial formula, expands a power of a sum of any number of terms, generalizing the binomial theorem from two terms to k terms.

Multiple comparisons problem

The multiple comparisons problem, also called the multiple testing problem, is the risk that testing many hypotheses at once inflates the chance of a false positive.

Multiple correspondence analysis

Multiple correspondence analysis (MCA), also known as homogeneity analysis or dual scaling, is a multivariate method for mapping categorical variables, standard for questionnaire and survey data.

Multiple factor analysis

Multiple factor analysis (MFA) is a multivariate statistical method analyzing several groups of variables measured on the same individuals, weighting each group so no single group dominates the analysis.

Multiple imputation

Multiple imputation is a statistical technique for handling missing data in which each missing value is replaced several times with plausible values, producing datasets analyzed and combined into one set of estimates.

Multiple imputation by chained equations

Multiple imputation by chained equations (MICE) is a statistical method for missing data that imputes each variable from a conditional model, producing several completed datasets.

Multiple Indicator Cluster Surveys

Multiple Indicator Cluster Surveys (MICS) is a global household survey program developed by UNICEF and conducted by national statistical offices, with 418 surveys in 123 countries by 2025.

Multiple integral

A multiple integral generalizes the single-variable integral to functions of several variables over regions of n-dimensional space, including double integrals over plane regions and triple integrals over solids, yielding volumes, masses, and probabilities.

Multiple scales method

The multiple scales method is a perturbation technique for differential equations that treats fast and slow timescales jointly, yielding uniformly valid approximations free of secular terms.

Multiple testing correction

Multiple testing correction, also called a multiple testing procedure, adjusts p-values or thresholds when many hypotheses are tested simultaneously, controlling either the family-wise error rate or the false discovery rate.

Multiple-point statistics

Multiple-point statistics (MPS) is a family of geostatistical simulation methods that generates spatial realizations from a training image rather than a variogram, formalized in 1993.

Multiple-scale analysis

Multiple-scale analysis is a perturbation method that treats fast and slow variables as independent to cancel secular terms, giving approximate solutions valid where regular perturbation expansions break down.

Multiple-try Metropolis

Multiple-try Metropolis (MTM) is a Markov chain Monte Carlo algorithm introduced by Liu, Liang, and Wong in 2000, drawing several candidate states each step and selecting among them by weight.

Multiplication

Multiplication is one of the four basic arithmetic operations, producing a product that represents repeated addition of one number a number of times equal to another.

Multiplication algorithm

A multiplication algorithm is a procedure for computing the product of two numbers or polynomials, from schoolbook long multiplication up to Karatsuba's and FFT-based methods approaching O(n log n).

Multiplication sign

The multiplication sign (×), also called the times sign, is a mathematical symbol for multiplication shaped as a diagonal cross, introduced by William Oughtred in 1631 and standard in elementary arithmetic.

Multiplication table

A multiplication table, also known as a times table, is a table showing the products of pairs of numbers, typically up to 10 or 12.

Multiplicative function

A multiplicative function is an arithmetic function on the positive integers with f(ab) = f(a)f(b) whenever gcd(a, b) = 1; examples include Euler's totient and the Möbius function.

Multiplicative group of integers modulo n

The multiplicative group of integers modulo n, also written Z n, is the finite abelian group of residue classes coprime to n, with order given by Euler's totient function.

Multiplicative inverse

A multiplicative inverse of a, written a⁻¹, is an element that multiplies a to give 1; for ordinary nonzero numbers it is the reciprocal, 1/a, and zero has none.

Multiplicative noise

Multiplicative noise is random forcing whose amplitude depends on the state of the system it perturbs, unlike additive noise, which has a constant amplitude. It appears in stochastic differential and partial differential equations.

Multiplicative order

The multiplicative order of an integer a modulo n is the smallest positive k with a^k ≡ 1 (mod n); it always divides Euler's totient φ(n).

Multiresolution analysis

Multiresolution analysis (MRA) is a framework in wavelet and harmonic analysis that decomposes a signal into coarse approximations plus detail components at successively finer scales.

Multiscale geographically weighted regression

Multiscale geographically weighted regression (MGWR) is a spatial statistics method, introduced by A. Stewart Fotheringham and colleagues in 2017, that extends geographically weighted regression by giving each predictor variable its own spatial bandwidth.