Mathematics and statistics

MCMC convergence diagnostics

MCMC convergence diagnostics are tools that check whether Markov chain Monte Carlo draws plausibly represent the target posterior distribution, such as R-hat and effective sample size.

McNemar's test

McNemar's test, also known as McNemar's chi-squared test, is a nonparametric statistical test for paired binary data, proposed by Quinn McNemar at Stanford in 1947.

Mealy machine

A Mealy machine, or Mealy automaton, is a finite-state machine whose output depends on its current state and current input, named after George H. Mealy, who introduced it in 1955.

Mean absolute error

Mean absolute error (MAE) is a scale-dependent measure of prediction accuracy, the average of absolute differences between predicted and true values, minimized by forecasting the median.

Mean absolute percentage error

The mean absolute percentage error (MAPE), also called the mean absolute percentage deviation, is a unit-free measure of forecast accuracy, most widely used in businesses.

Mean centering

Mean centering is a statistical preprocessing step that subtracts a variable's mean from each observation, giving transformed values that average to zero; it is used in regression and PCA.

Mean curvature

Mean curvature is the average of the two principal curvatures of a surface at a point, one of the two standard curvature quantities in classical surface theory.

Mean curvature flow

Mean curvature flow is a geometric evolution process in which every point of a surface moves in the normal direction at a speed equal to the local mean curvature.

Mean first passage time

The mean first passage time, also called the mean hitting time, is the expected number of steps a Markov chain takes to reach a given state from another specified state.

Mean imputation

Mean imputation is a statistical method for handling missing data that replaces each missing value with the mean of that variable's observed values, keeping incomplete records in an analysis.

Mean squared error

Mean squared error (MSE), also called mean squared deviation, is the expected squared difference between an estimator or prediction and the true value, decomposing into variance plus squared bias.

Mean time between failures

Mean time between failures (MTBF), also called mean time before failure, is a reliability metric: the expected time between successive failures of a repairable item that can be restored to service.

Mean value theorem

The mean value theorem, also called Lagrange's mean value theorem, is a calculus theorem guaranteeing a point where instantaneous rate of change equals average rate of change.

Measurable cardinal

A measurable cardinal is an uncountable cardinal carrying a nontrivial two-valued measure, introduced by Stanisław Ulam in 1930; its existence cannot be proved in ZFC and contradicts V = L.

Measurable function

A measurable function, also called a measurable map, is a function between measurable spaces that pulls measurable sets back to measurable sets, the functions that can be integrated.

Measure (mathematics)

In mathematics, a measure is a function assigning a nonnegative number or infinity to subsets of a set, generalizing length, area, and volume; measure theory underlies integration and probability.

Measure algebra

A measure algebra is a Boolean σ-algebra with a strictly positive measure, built from measurable sets identified when they differ only by a set of measure zero.

Measurement invariance testing

Measurement invariance testing is a psychometric procedure that checks whether a scale measures the same construct with the same parameters in different groups, using multigroup confirmatory factor analysis.

Measurement system analysis

Measurement system analysis (MSA) is the statistical evaluation of a measurement process, best known for its Gauge R&R study, which separates repeatability, reproducibility, and part-to-part variation in manufacturing.

Measures of national income and output

Measures of national income and output, chiefly GDP, are national accounting statistics quantifying an economy's production, income, and expenditure under the System of National Accounts.

Mechanical calculator

A mechanical calculator, or calculating machine, performs arithmetic using gears and drums rather than electronics; first built in 1623, it was displaced by electronic calculators in the 1960s.

Medial axis transform

The medial axis transform (MAT) is a shape representation describing an object by the centers of its maximally inscribed balls and their radii, introduced by Harry Blum in 1967.

Median

The median, also called the median average, is the middle value of an ordered data set and the 50th percentile, one of three common measures of central value.

Median (geometry)

A median of a triangle is the line segment joining a vertex to the midpoint of the opposite side. Each triangle has three medians, meeting at the centroid.

Median absolute deviation

The median absolute deviation (MAD) is a robust measure of statistical dispersion, computed as the median of absolute deviations from the data's median, resisting distortion by outliers.

Median test

The median test, also known as Mood's median test, is a nonparametric statistical test of whether two or more independent samples come from populations with the same median.

Mediated moderation

Mediated moderation is a statistical analysis method in psychology and the social sciences that tests whether the interaction effect of a predictor and moderator operates through a mediator.

Mediation (statistics)

Mediation analysis, also known as mediation or statistical mediation, decomposes an exposure's total effect on an outcome into indirect effects through a mediator and direct effects that bypass it.

Mediation model

A mediation model is a statistical model that splits an independent variable's effect on an outcome into direct and indirect pathways through an intermediate mediator variable.