Mathematics and statistics

Doob decomposition theorem

The Doob decomposition theorem states that any discrete-time stochastic process splits uniquely into a martingale and a predictable process, a result Joseph Doob published in 1953.

Doob–Meyer decomposition theorem

The Doob–Meyer decomposition theorem, the continuous-time extension of Doob's 1953 decomposition, states a class D submartingale is uniquely a martingale plus a predictable increasing process.

Doob's martingale convergence theorems

Doob's martingale convergence theorems are results in probability theory, due to Joseph Doob, giving conditions under which a martingale converges almost surely or in L¹.

Doob's martingale inequality

Doob's martingale inequality is a result in probability theory, named after Joseph L. Doob, bounding the running maximum of a martingale by its final value.

Dose-response meta-analysis

Dose-response meta-analysis is a statistical method in evidence synthesis that combines several studies to estimate how the risk of an outcome changes with exposure dose.

Dot plot (statistics)

A dot plot is a statistical graphic displaying each data value as a dot on a number line, with two types: the Wilkinson distribution plot and the Cleveland dot chart.

Dot product

The dot product, also called the scalar product, is an operation on two vectors that returns a single number, the product of their lengths and the cosine of the angle between them.

Double counting (proof technique)

Double counting is a proof technique in combinatorics that counts the elements of one finite set in two different ways and equates the results, yielding identities, inequalities, and nonexistence claims.

Double factorial

The double factorial of a nonnegative integer n, written n!!, is the product of all positive integers up to n with the same parity as n.

Double sampling (statistics)

Double sampling, also called two-phase sampling, is a survey sampling method that takes cheap auxiliary measurements on a large sample, then measures costly study variables on a subsample.

Double-precision floating-point format

Double-precision floating-point format, known as binary64, is the 64-bit number format defined by IEEE 754 that offers about 15 to 17 significant decimal digits of precision.

Doubling time

Doubling time, also called doubling period, is the time an exponentially growing quantity needs to double, given by ln 2 divided by the growth rate.

Doubly robust estimation

Doubly robust estimation is a statistical method for estimating causal effects or means with missing data, remaining unbiased if either the outcome model or the propensity model is correct.

Doubly stochastic matrix

A doubly stochastic matrix, also called a bistochastic matrix, is a square matrix of nonnegative numbers in which every row and every column sums to 1.

Doxastic logic

Doxastic logic is a branch of modal logic that formalizes reasoning about belief, initiated by Jaakko Hintikka in 1962 and distinguished from knowledge by beliefs that can be false.

DPLL algorithm

The DPLL algorithm (Davis–Putnam–Logemann–Loveland) is a complete backtracking search procedure for deciding whether a Boolean CNF formula is satisfiable, published in 1960–1962 by Davis, Putnam, Logemann, and Loveland.

Drazin inverse

The Drazin inverse is a unique pseudoinverse of a square matrix that inverts its invertible part and annihilates its nilpotent part, introduced by M. P. Drazin in 1958.

Drinfeld center

The Drinfeld center of a monoidal category is a braided monoidal category whose objects are pairs with half-braidings, the categorical counterpart of Drinfeld's quantum double of a Hopf algebra.

Drinfeld double

The Drinfeld double, also called the quantum double, is a Hopf algebra built from a Hopf algebra and its dual, introduced by Vladimir Drinfeld in 1986.

Drools

Drools, also known as JBoss Rules, is an open source rule engine and business rule management system written in Java, begun in 2001 and now part of Apache KIE.

DSatur

DSatur (DSATUR, for degree of saturation) is a greedy heuristic for graph coloring proposed by Daniel Brélaz in 1979, provably optimal on bipartite, cycle, wheel, and chordal graphs.

Du Val singularity

A Du Val singularity, also called a rational double point or Kleinian singularity, is a surface singularity classified by the Dynkin diagrams A, D, and E, named after Patrick Du Val.

Dual basis

A dual basis is a basis of the dual space V matched to a basis of V: each functional gives 1 on one basis vector and 0 on the others.

Dual dynamic programming

Dual dynamic programming (DDP), also called stochastic dual dynamic programming (SDDP), is an algorithm for multistage stochastic optimization that approximates future costs with Benders cuts, developed for Brazilian hydrothermal power planning.

Dual graph

The dual graph, or planar dual, of a planar graph has one vertex for each face and one edge for each pair of faces sharing an edge.

Dual map

The dual map, also called the transpose, is the linear map between dual spaces that a linear map induces, running in the opposite direction; its matrix is the transpose.

Dual matroid

The dual matroid of a matroid M is the matroid M on the same ground set whose bases are the complements of M's bases, introduced by Hassler Whitney in 1935.

Dual module

The dual module of a module M is Hom_R(M, R), the module of linear maps from M to the ring R, generalizing dual vector spaces.

Dual number

A dual number is an expression of the form a + εb, where ε is nonzero with ε² = 0, introduced by Clifford in 1873 and used in automatic differentiation.