Mathematics and statistics

Bernoulli model

The Bernoulli model is a statistical model for binary data where each observation is a success or failure with fixed success probability, underlying binomial and logistic models.

Bernoulli number

The Bernoulli numbers are a sequence of rational numbers introduced by Jacob Bernoulli to sum powers of integers, appearing in the Euler–Maclaurin formula and the Riemann zeta function.

Bernoulli numbers

The Bernoulli numbers are a sequence of rational numbers named for Jacob Bernoulli, who introduced them in his 1713 Ars Conjectandi to compute sums of powers of integers.

A Bernoulli process is a sequence of independent Bernoulli trials, each with only two outcomes and the same success probability p, named after Jacob Bernoulli, who proved the weak law of large numbers.

Bernoulli shift

The Bernoulli shift is the shift map on infinite sequences of independent random variables, the canonical deterministic system reproducing independent random sampling, with entropy equal to Shannon entropy.

Bernoulli trial

A Bernoulli trial, also known as a binomial trial, is a random experiment with exactly two outcomes, success and failure, where the success probability p stays fixed.

Bernstein inequalities

The Bernstein inequalities are exponential concentration bounds for sums of independent random variables using both variance and a bound on each summand, introduced by Sergei Bernstein in 1924.

Bernstein polynomial

A Bernstein polynomial is a polynomial expressed as a combination of Bernstein basis functions on the unit interval, numerically stable and standard in computer-aided geometric design as the Bézier form.

Bernstein polynomials

Bernstein polynomials are polynomials formed from nonnegative Bernstein basis functions on [0, 1], introduced by Sergei Bernstein in 1912 and converging uniformly to any continuous function.

Bernstein–von Mises theorem

The Bernstein–von Mises theorem states that in large samples the Bayesian posterior is approximately normal, centered at the maximum likelihood estimator, regardless of the prior used.

Bernstein's theorem on monotone functions

Bernstein's theorem on monotone functions, also called the Hausdorff-Bernstein-Widder theorem, is a result of analysis stating that a function is completely monotone if and only if it is the Laplace transform of a non-negative measure.

Berry–Esseen theorem

The Berry–Esseen theorem, or Berry–Esseen inequality, is a probability result giving a finite-sample bound on how far standardized sums of independent variables stray from the normal distribution.

Bertini (software)

Bertini is a software package for numerical algebraic geometry that solves polynomial systems by homotopy continuation, written in C and distributed free of charge by four researchers.

Bertrand paradox (probability)

The Bertrand paradox, noted by Joseph Bertrand in 1889, shows that a random chord in a circle exceeding the inscribed triangle's side gives three defensible probabilities: 1/3, 1/2, and 1/4.

Bertrand's box paradox

Bertrand's box paradox is a probability problem posed by Joseph Bertrand in 1889: after drawing a gold coin from one of three boxes, the other coin is gold with probability 2/3.

Bertrand's postulate

Bertrand's postulate, also called the Bertrand–Chebyshev theorem, states that for every n > 1 there is a prime between n and 2n; conjectured in 1845 by Joseph Bertrand and first proved by Chebyshev in 1850.

Besov space

A Besov space is a space of functions or distributions whose smoothness is measured by a modulus of smoothness; it contains Hölder and Sobolev spaces as special cases.

Bessel function

The Bessel function, also called a cylinder function, is a solution of Bessel's differential equation, used across applied mathematics and physics for cylindrically symmetric problems such as vibrating drumheads and coaxial cables.

Bessel's correction

Bessel's correction is the use of n − 1 instead of n in the sample variance denominator, giving an unbiased estimator of the population variance.

Oct 10, 2026

Best linear unbiased estimator

The best linear unbiased estimator (BLUE) is the lowest-variance linear unbiased estimator of a linear-model parameter; by the Gauss–Markov theorem, ordinary least squares is BLUE under standard assumptions.

Best linear unbiased prediction

Best linear unbiased prediction (BLUP) is a statistical method for predicting random effects, such as breeding values, in a linear mixed model, standard in animal breeding.

Beta distribution

The beta distribution is a family of continuous probability distributions on the interval from 0 to 1, defined by two shape parameters and used to model proportions and probabilities.

Beta function

The beta function, also called the Euler beta function, is a special function B(a, b) defined by an integral and equal to Γ(a)Γ(b)/Γ(a + b).

Beta negative binomial distribution

The beta negative binomial distribution (BNB) is a three-parameter count distribution formed when a negative binomial success probability follows a beta distribution, giving heavier tails than the negative binomial.

Beta regression

Beta regression, or the beta regression model, is a maximum-likelihood regression method for continuous responses in the open unit interval, such as rates and proportions.

Beta-binomial distribution

The beta-binomial distribution is a discrete distribution for binomial counts whose success probability is drawn from a beta distribution, used to model overdispersion in count data.

Betti number

A Betti number, named for Enrico Betti and formalized by Henri Poincaré, is a topological invariant counting a space's independent cycles: components, loops, and cavities.

Betweenness centrality

Betweenness centrality is a graph metric that counts how often a node lies on shortest paths between other nodes, identifying brokers who control communication in networks.

Bézier curve

A Bézier curve, also called a Bernstein-Bézier curve, is a parametric curve shaped by control points, developed in the 1960s and widely used in computer-aided design, vector graphics, and font outlines.