Mathematics and statistics

Axiom schema of replacement

The axiom schema of replacement, also called the axiom of replacement, states that in Zermelo–Fraenkel set theory the image of a set under a definable function is a set.

Axiom schema of specification

The axiom schema of specification, also called the axiom schema of separation or subset axiom, is a Zermelo–Fraenkel axiom, introduced by Zermelo in 1908 to block Russell's paradox.

Axiomatic method

The axiomatic method builds a body of knowledge from a small set of axioms, deriving every other claim by explicit rules of inference, from Euclid's Elements onward.

Axiomatic system

An axiomatic system, or axiom system, is a body of knowledge organized as primitive terms, axioms accepted without proof, and rules of inference that derive further statements called theorems.

Axonometric projection

Axonometric projection is an orthographic method of showing a 3D object at an angle so one view reveals several sides, with subtypes isometric, dimetric, and trimetric.

Azuma's inequality, more commonly called the Azuma–Hoeffding inequality, is a concentration inequality stating that a martingale with bounded increments is unlikely to move far from its starting value.

B-spline

A B-spline, named by Schoenberg as a shortening of basic spline, is a piecewise polynomial basis for spline spaces, standard in computer-aided design through NURBS and used in finite element analysis.

Baby-step giant-step

Baby-step giant-step is a deterministic algorithm introduced by Daniel Shanks in 1971 that computes discrete logarithms in a cyclic group in square-root time, at the cost of comparable storage.

Babylonian cuneiform numerals

Babylonian cuneiform numerals are the base 60 place-value number system of ancient Mesopotamia, written with just two wedge signs into clay and surviving today in minutes and seconds.

Babylonian mathematics

Babylonian mathematics, also called Assyro-Babylonian mathematics, is the mathematics recorded in cuneiform on clay tablets in ancient Mesopotamia, best known for its base 60 number system.

Back projection (tomography)

Back projection is a tomographic image reconstruction method that distributes each ray sum along its line and sums over angles; with filtering it became the standard CT method for four decades.

Backtesting

Backtesting is a validation method that evaluates a risk model, trading strategy, or forecasting rule by applying it to historical data; in banking, it compares daily value-at-risk forecasts with actual losses.

Backtracking line search

Backtracking line search is an optimization procedure that repeatedly multiplies a trial step length by a constant factor until the Armijo sufficient-decrease condition holds, accepting the first adequate step.

Backward differentiation formula

The backward differentiation formula (BDF) is a family of implicit linear multistep methods for stiff ordinary differential equations, first used in Curtiss and Hirschfelder's 1952 paper.

Backward error analysis

Backward error analysis is a numerical analysis technique that judges a computed result by how much the input data must be perturbed for it to be exact.

Backward Euler method

The backward Euler method, also called implicit Euler, is a first-order implicit method for integrating ordinary differential equations, valued for its stability on stiff problems.

Backward induction

Backward induction is a game theory method for solving sequential games by determining optimal moves at each decision node, working from the end of the game back to the start.

Backward stochastic differential equation

A backward stochastic differential equation (BSDE) is a stochastic equation solved backward from a terminal condition, used in finance, optimal control, and gene expression modeling.

Bad Science (book)

Bad Science is a 2008 popular-science book by British doctor Ben Goldacre that teaches readers to judge medical claims by dissecting bad evidence and health reporting.

Badan Pusat Statistik

Badan Pusat Statistik (BPS), or Statistics Indonesia, is the government agency producing Indonesia's official statistics under Law Number 16 of 1997 and coordinating the Indonesian National Statistical System.

Bailey–Borwein–Plouffe formula

The Bailey–Borwein–Plouffe formula (BBP) is a 1995 series for π that computes hexadecimal or binary digits of π starting at any position without earlier digits.

Baire property

The Baire property, also called the property of Baire, is a regularity property of subsets of a topological space: the set differs from an open set only by a meager set.

Baire space (set theory)

Baire space in set theory is the set of all infinite sequences of natural numbers with the product topology; it is homeomorphic to the irrational real numbers.

Baker–Campbell–Hausdorff formula

The Baker–Campbell–Hausdorff formula, or BCH formula, expresses log(exp(X)exp(Y)) as a series of nested Lie brackets with rational coefficients, converging for X and Y close to zero and used across physics and control theory.

Baker's theorem

Baker's theorem is a result in transcendental number theory giving explicit lower bounds for nonzero linear forms in logarithms of algebraic numbers, proved by Alan Baker in 1966.

Balanced design

Balanced design is a statistical experimental design in which every combination of factor levels receives the same number of experimental units, making treatment comparisons equally precise.

Balanced incomplete block design

A balanced incomplete block design (BIBD) is a statistical design assigning v treatments to blocks too small to hold all, with every pair occurring equally often.

Balanced repeated replication

Balanced repeated replication, also called balanced half-sample replication, is a resampling method for estimating the sampling variance of statistics from stratified surveys with two primary sampling units per stratum.

Balanced sampling

Balanced sampling is a probability sampling method in which weighted sample totals of chosen auxiliary variables exactly match known population totals, reducing the variance of estimators of correlated variables.