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branching process


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stochastic process

probability

Markov chain

Francis Galton (1822—1911) biostatistician, human geneticist, and eugenicist

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'branching process' can also refer to...

branching process

branching process

Statistical distributions of earthquake numbers: consequence of branching process

Leading Process Branch Instability in Lis1+/− Nonradially Migrating Interneurons

Empty confidence sets for epidemics, branching processes and Brownian motion

Processing of Branched DNA Intermediates by a Complex of Human FEN-1 and PCNA

Sensitivity analysis of a branching process evolving on a network with application in epidemiology

A theoretical framework for evolutionary economic geography: industrial dynamics and urban growth as a branching process

Punctuated Equilibrium Behavior and Zipf's Law in the Stochastic Branching Process Model of Phylogeny

Branching process models for surveillance of infectious diseases controlled by mass vaccination

Hypothesis testing for neural cell growth experiments using a hybrid branching process model

A branching process model for the analysis of abortive colony size distributions in carbon ion-irradiated normal human fibroblasts

The allele distribution in next-generation sequencing data sets is accurately described as the result of a stochastic branching process

Nine new metal-poor stars on the subgiant and red horizontal branches with high levels of r-process enhancement★

A composite likelihood approach to the analysis of longitudinal clonal data on multitype cellular systems under an age-dependent branching process

The s-process in low-metallicity stars – III. Individual analysis of CEMP-s and CEMP-s/r with asymptotic giant branch models

The branchings of the main s-process: their sensitivity to α-induced reactions on 13C and 22Ne and to the uncertainties of the nuclear network

 

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A stochastic process with varying numbers of states. Consider a population in which each individual has probability pk of providing k descendants in the next generation. Let Xj be the number of individuals in the jth generation. The sequence X1, X2,…, is a Markov process known as a branching process. This formulation was originally suggested by Galton and Henry Watson in 1874 in the context of the extinction of surnames, and may be referred to as the Galton–Watson model. Extinction is certain if and only if and otherwise the probability of extinction is equal to P, the solution (between 0 and 1) of .

Subjects: Probability and Statistics.


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