6,052 articles
Two-way analysis of variance
Two-way analysis of variance, or two-way ANOVA, is a statistical method for testing how two factors each with multiple levels affect a response, including interactions between them.
Two's complement
Two's complement is the standard binary representation of signed integers, where negation flips all bits and adds 1, and it has a single representation of zero.
Type (model theory)
In model theory, a type, or complete type, is a set of first-order formulas describing a possible element or tuple of a structure, realized when some tuple satisfies them all.
Type I and type II errors
Type I and type II errors, also called type 1 and type 2 errors, are the false positive and false negative mistakes a statistical hypothesis test can make.
Type inference
Type inference, also known as type reconstruction or type deduction, is the process by which a compiler determines an expression's type without explicit programmer annotations, as in ML and Haskell.
Type theory
Type theory, or the theory of logical types, is a formal system where every entity carries a type, serving as a foundation for mathematics and proof assistants like Lean and Rocq.
Typical sequence
A typical sequence is a long sequence of symbols drawn from a probability distribution whose sample entropy is close to the source's entropy, central to the asymptotic equipartition property.
U-statistic
A U-statistic is an estimator averaging a kernel function over all subsamples of fixed size m from the data, introduced by Wassily Hoeffding in 1948 and underlying the Mann–Whitney and Wilcoxon tests.
UK Data Service
The UK Data Service is the United Kingdom's principal national repository of economic, population, and social research data, founded in 2012 and funded by UKRI through the Economic and Social Research Council.
UK Statistics Authority
The UK Statistics Authority (UKSA) is an independent non-ministerial UK government department, established in 2008 and accountable to Parliament, which safeguards official statistics through the Office for National Statistics and the Office for Statistics Regulation.
Ulam spiral
The Ulam spiral, or prime number spiral, is a square spiral of integers with primes marked, whose primes cluster along diagonal lines; it was drawn by Stanislaw Ulam in 1963.
Ultimate L program
The Ultimate L program is a research program in mathematical logic led by W. Hugh Woodin, seeking an inner model compatible with all large cardinal axioms.
Ultrafilter
An ultrafilter is a maximal filter on a set: for every subset, exactly one of it and its complement belongs. It connects logic through ultraproducts and topology through compactification.
Ultrametric space
An ultrametric space is a metric space in which the triangle inequality is replaced by the stronger ultrametric inequality; its basic example is the p-adic metric on the rationals.
Ultrapower
An ultrapower is a model-theoretic construction building a new structure from many copies of one structure using an ultrafilter, the special case of an ultraproduct behind nonstandard analysis.
Ultraproduct
An ultraproduct is a model theory construction combining an infinite family of mathematical structures into one via an ultrafilter, preserving first-order properties by Łoś's theorem, defined by Jerzy Łoś in 1955.
Umbral calculus
Umbral calculus, also known as Blissard's symbolic method, is an algebraic technique treating a sequence's index as an exponent, made rigorous by Gian-Carlo Rota in the 1970s.
Umbrella trial
An umbrella trial is a master protocol clinical trial that evaluates multiple investigational drugs in a single disease population, matching each patient to a treatment by their tumor's biomarker.
UML state machine
The UML state machine, also called a UML statechart, is a Unified Modeling Language behavioral model that describes system behavior through states, events, and transitions, extending David Harel's 1987 statecharts.
UN Comtrade
UN Comtrade, the United Nations Commodity Trade Statistics Database, holds official annual and monthly merchandise trade data from about 200 countries, with records dating back to 1962.
Unary numeral system
The unary numeral system, also known as base 1, is the simplest numeral system, representing each natural number by repeating a single symbol that many times, as in tally marks.
Unary operation
A unary operation, also called a unary or monadic operator, is a function with exactly one input, such as negation, square root, or multiplicative inverse in a group.
Unbiased estimation of standard deviation
Unbiased estimation of standard deviation corrects the sample standard deviation s, which underestimates σ because the square root is nonlinear; the c₄ factor applies for normal populations.
Unbiased estimator
An unbiased estimator is a statistic used to estimate an unknown quantity whose expected value equals that quantity for every possible value, so errors average to zero across repeated samples.
Uncertainty quantification
Uncertainty quantification (UQ) is the science of characterizing, propagating, and reducing uncertainty in mathematical and computational models, using tools like Monte Carlo methods, polynomial chaos, and Bayesian inference.
Uncountable set
An uncountable set is an infinite set too large to count, whose elements cannot be paired with the natural numbers, a fact first shown by Cantor in 1874.
Undecidable problem
An undecidable problem, also known as an unsolvable or recursively undecidable problem, is a decision problem for which no algorithm always halts with a correct yes-or-no answer, a limit proven by Turing's halting problem.
Unexpected hanging paradox
The unexpected hanging paradox, also called the surprise examination paradox, is an epistemic paradox in which a prisoner's backward reasoning proves his surprise hanging impossible, yet it surprises him.
Unification (computer science)
Unification in computer science is the algorithmic problem of finding a substitution making two logical expressions identical, introduced by Robinson in 1965 for resolution theorem proving.
Uniform algebra
A uniform algebra is a closed subalgebra of continuous functions on a compact Hausdorff space, containing the constants and separating points, studied for uniform approximation.