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The recovery of the root of a tree

Published online by Cambridge University Press:  14 July 2016

John Haigh
John Haigh*
Affiliation:
University of Sussex
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Abstract

A population which develops as a linear birth process from one individual gives rise to a family tree of size N which shows the relationships of the N members to each other. If this tree is given, but with no a priori information of which point is the root (the original member) we seek to utilize our knowledge of the stochastic manner in which the tree grew to estimate this root. A maximum likelihood estimate is obtained, and the probabilities that this estimate is the true kth point, or a member of the true rth generation are obtained as functions of N. As N → ∞ these probabilities converge to non-zero values for any fixed k, r, which are surprisingly large—for example, when k is 1, the limiting value is 1 — loge2 ≈ .30685.

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 1 , April 1970 , pp. 79 - 88
Copyright
Copyright © Applied Probability Trust 

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References

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