statistics, a Pólya urn model (also known as a Pólya urn scheme or simply as Pólya's urn), named after George Pólya, is a family of urn models that can be...

ball of the same color is added to the urn. Hence, the number of total balls in the urn grows. See Pólya urn model. binomial distribution: the distribution...

George Pólya (/ˈpoʊljə/; Hungarian: Pólya György, pronounced [ˈpoːjɒ ˈɟørɟ]; December 13, 1887 – September 7, 1985) was a Hungarian-American mathematician...

binomial can also be motivated by an urn model - or more specifically a basic Pólya urn model. Consider an urn initially containing α {\displaystyle...

be motivated via an urn model for positive integer values of α and β, known as the Pólya urn model. Specifically, imagine an urn containing α red balls...

multinomial can also be motivated by an urn model - or more specifically a basic Pólya urn model. Consider an urn initially containing ∑ i = 0 m α i {\displaystyle...

compound multinomial distribution (DCM) or multivariate Pólya distribution (after George Pólya). It is a compound probability distribution, where a probability...

etc.) given a fixed number of total occurrences, sampling using a Pólya urn model (in some sense, the "opposite" of sampling without replacement) Categorical...

variables that are not statistically independent, for example the Pólya urn model. A random variable X has a Bernoulli distribution if Pr(X = 1) = p...

way to generate the Beta distribution is by Pólya urn model. According to this method, one start with an "urn" with α "black" balls and β "white" balls...

mappings without needing grammatical structure. Using the Price equation and Pólya urn dynamics, researchers have created a system which not only predicts future...

be a particular case of the Pólya Filter (built around the famous combinatorial scheme known as the Pólya Urn). The Pólya Filter is able to adapt the...

process is as a modified Pólya urn scheme sometimes called the Blackwell–MacQueen sampling scheme. Imagine that we start with an urn filled with α {\displaystyle...

its first appearance in 1923 in the celebrated urn model of the Hungarian mathematician György Pólya in 1923. The master equation method, which yields...

Blackwell, David; MacQueen, James B. (1973). "Ferguson distributions via Polya urn schemes". Ann. Stat. 1 (2): 353–355. doi:10.1214/aos/1176342372. A. Gelman;...

an urn, then replaced in the urn along with an additional ball of the same color, simulating the probabilistic nature of tag reuse. This simple model, however...

\left\{X_{i}\right\}_{i\in \mathbb {N} }} is an exchangeable sequence. This model is called Polya's urn. Let ( X , Y ) {\displaystyle (X,Y)} have a bivariate normal...

a year earlier by Fred Hoppe, using an "urn scheme" akin to Pólya's urn. In comparison with Hoppe's urn model, the Chinese restaurant process has the...

\end{aligned}}} Pólya's urn contains a number of different-coloured marbles; at each iteration a marble is randomly selected from the urn and replaced with...

Multivariate Pareto distribution Multivariate Pólya distribution Multivariate probit – redirects to Multivariate probit model Multivariate random variable Multivariate...

"Functional limit theorems for multitype branching processes and generalized Pólya urns". Stochastic Processes and Their Applications. 110 (2): 177–245. doi:10...

distributions of time intervals for the occurrence of successive accidents in a generalized Polya urn scheme", Annals of Mathematical Statistics, 26, 705–720...

1925–1932 C. Brian Haselgrove mathematician best known for disproving the Pólya conjecture in 1958 Thomas Hayter, bishop of Norwich 1749–61, bishop of London...