Mathematics and statistics

Bayesian probability

Bayesian probability, also known as Bayesian probability theory or personal probability, is an interpretation of probability as a degree of belief, updated in light of new evidence by Bayes' theorem.

Bayesian programming

Bayesian programming is a statistical modeling approach in which a programmer writes a model as a program containing random variables, and a general-purpose inference engine updates it from data.

Bayesian regression

Bayesian regression fits a regression model by combining a prior on its parameters with the data's likelihood, yielding a full posterior distribution rather than a point estimate.

Bayesian reliability and safety analysis software

Bayesian reliability and safety analysis software is a family of tools that estimate failure rates and system risk from limited data, including SCRAM, XFTA, RADYBAN, BAHAMAS, and SAFEST.

Bayesian sampling is a class of statistical methods that draws random samples from a posterior distribution, replacing intractable integrals with sample averages, most often via Markov chain Monte Carlo.

Bayesian search theory

Bayesian search theory is the branch of operations research that plans searches for lost objects, updating a probability map of possible locations after each unsuccessful search.

Bayesian software for epidemiological modeling

Bayesian software for epidemiological modeling is the family of packages that fit epidemic and disease-transmission models to data using Bayesian inference, estimating transmission rates, reproduction numbers, and delay distributions with uncertainty quantified through posterior distributions.

Bayesian statistics

Bayesian statistics is an approach to data analysis in which prior knowledge about a model's parameters is combined with observed data via Bayes' theorem, yielding a posterior distribution for inference.

Bayesian underwater search

Bayesian underwater search applies Bayesian statistics to locating objects lost at sea, such as shipwrecks and crashed aircraft, and famously found the USS Scorpion and Air France Flight 447.

Bayesianism

Bayesianism is a family of positions in statistics and epistemology holding that probability measures rational degrees of belief, revised by conditionalizing on evidence through Bayes' theorem.

BCH code

A BCH code, or Bose-Chaudhuri-Hocquenghem code, is a cyclic error-correcting code over a finite field, described in 1959 and 1960 and widely used in communication systems and data storage.

Beal conjecture

The Beal conjecture is an unsolved number theory problem, posed by Andrew Beal in 1993, stating that A^x + B^y = C^z with exponents above 2 forces a common prime factor.

Beam search

Beam search is a heuristic search algorithm that keeps only the k most promising partial candidates at each step, commonly used to decode neural sequence models.

Begriffsschrift

Begriffsschrift (German for "concept-script") is a formal logical system and two-dimensional notation introduced by Gottlob Frege in his 1879 booklet, containing the first quantifier in formal logic and the first logical system with relations.

Beilinson–Bernstein localization

Beilinson–Bernstein localization is a theorem in geometric representation theory, announced in 1981, stating that Lie algebra representations are equivalent to D-modules on the flag variety.

Belief propagation

Belief propagation, also known as the sum-product algorithm, is a message-passing algorithm introduced by Judea Pearl in 1988 for computing marginal probabilities on graphical models.

Bell number

The Bell number B(n) is the number of ways to partition a set of n labeled elements into non-empty subsets; the sequence begins 1, 1, 2, 5, 15.

Bell numbers

The Bell numbers, named for mathematician Eric Temple Bell, count the partitions of a set of n labeled elements, beginning 1, 1, 2, 5, 15, 52.

Bell polynomials

Bell polynomials are polynomials introduced by Eric Temple Bell in 1934 that encode the combinatorics of set partitions, appearing in the Faà di Bruno formula and moment–cumulant relations.

Bellman–Ford algorithm

The Bellman–Ford algorithm, also called Bellman–Ford–Moore, computes shortest paths from a source in directed graphs whose edge weights may be negative, detects negative cycles, and runs in O(V·E) time.

Ben Green (mathematician)

Ben Joseph Green, born 1977 in Bristol, is a British mathematician who proved the Green–Tao theorem with Terence Tao in 2004 and is Waynflete Professor at Oxford.

Benders decomposition

Benders decomposition is an optimization method that solves large mixed-integer programs by splitting them into a master problem and a subproblem, introduced by J. F. Benders in 1962.

Benford's law

Benford's law, also called the first-digit phenomenon or Newcomb–Benford law, holds that leading digits follow log10(1 + 1/d); noted by Newcomb in 1881 and rediscovered by Benford in 1938, it is widely used in fraud detection.

Benjamin–Bona–Mahony equation

The Benjamin–Bona–Mahony equation, also known as the regularized long-wave equation, is a nonlinear partial differential equation introduced in 1972 as a model for long water waves.

Benjamini–Hochberg procedure

The Benjamini–Hochberg procedure is a step-up multiple-testing method that controls the false discovery rate, introduced by Yoav Benjamini and Yosef Hochberg in 1995 and widely used in genomics.

Bergman space

The Bergman space is the Hilbert space of holomorphic functions on a domain that are square-integrable with respect to area measure, with a reproducing kernel called the Bergman kernel.

Berkovich space

A Berkovich space is an analytic space over a non-archimedean valued field such as the p-adic numbers, introduced by Vladimir Berkovich in 1990, whose points are multiplicative seminorms.

Berlekamp–Massey algorithm

The Berlekamp–Massey algorithm finds the shortest linear feedback shift register that generates a given sequence over a field, developed by Berlekamp in 1968 and Massey in 1969.

Bernhard Riemann

Bernhard Riemann (Georg Friedrich Bernhard Riemann) was a German mathematician at Göttingen who defined the Riemann integral, founded Riemannian geometry, and posed the unproven Riemann hypothesis.