Parameter estimation in topological analysis of binary tree structures
type: Item
instance of: scholarly article
title: Parameter estimation in topological analysis of binary tree structures
zbMATH Open document ID: 0613.92001
DOI: 10.1007/BF02460126
author: Ronald W. H. Verwer
author: Jaap van Pelt
author: André J. Noest
published in: Bulletin of Mathematical Biology
publication date: 1987-01-01T00:00:00Z
review text: Different types of random binary topological trees (like neuronal processes and rivers) occur with relative frequencies that can be explained in terms of growth models. It will be shown how the model parameter determining the mode of growth can be estimated with the maximum likelihood procedure from observed data. Monte Carlo simulations were used to study the distributional properties of this estimator which appeared to have a negligible bias. It is shown that the minimum chi-square procedure yields an estimate that is very close to the maximum likelihood estimate. Moreover, the goodness- of-fit of the growth model can be inferred directly from the chi-square statistic. To illustrate the procedure we examined axonal trees from the goldfish tectum. A notion of complete partition randomness is presented as an alternative to our growth hypotheses.
Mathematics Subject Classification ID: 92B05
Mathematics Subject Classification ID: 62P10
Mathematics Subject Classification ID: 92F05
zbMATH DE Number: 3993344
zbMATH Keywords: random binary topological trees
zbMATH Keywords: growth models
zbMATH Keywords: maximum likelihood procedure
zbMATH Keywords: minimum chi-square procedure
zbMATH Keywords: goodness-of-fit
zbMATH Keywords: axonal trees
Wikidata QID: Q52610280
MaRDI profile type: Publication
cites work: Minimum chi-square, not maximum likelihood!
cites work: Monte Carlo Confidence Intervals
cites work: Q4124103
cites work: Q4101268
cites work: Q5842591
cites work: Q5185878
cites work: The probabilities of rooted tree-shapes generated by random bifurcation
cites work: Q3672893
cites work: The exact probabilities of branching patterns under terminal and segmental growth hypotheses
cites work: Growth models (including terminal and segmental branching) for topological binary trees
cites work: Topological properties of binary trees grown with order-dependent branching probabilities
cites work: Q5561562
full work available at URL: https://doi.org/10.1007/bf02460126
OpenAlex ID: W4230914356
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description: scientific article; zbMATH DE number 3993344