Dependent radius marks of Laguerre tessellations: a case study
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10430531" target="_blank" >RIV/00216208:11320/21:10430531 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xd1~FGywYb" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xd1~FGywYb</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1111/anzs.12314" target="_blank" >10.1111/anzs.12314</a>
Alternative languages
Result language
angličtina
Original language name
Dependent radius marks of Laguerre tessellations: a case study
Original language description
We study a particular marked three-dimensional point process sample that represents a Laguerre tessellation. It comes from a polycrystalline sample of aluminium alloy material. The 'points' are the cell generators while the 'marks' are radius marks that control the size and shape of the tessellation cells. Our statistical mark correlation analyses show that the marks of the sample are in clear and plausible spatial correlation: the marks of generators close together tend to be small and similar and the form of the correlation functions does not justify geostatistical marking. We show that a simplified modelling of tessellations by Laguerre tessellations with independent radius marks may lead to wrong results. When we started from the aluminium alloy data and generated random marks by random permutation we obtained tessellations with characteristics quite different from the original ones. We observed similar behaviour for simulated Laguerre tessellations. This fact, which seems to be natural for the given data type, makes fitting of models to empirical Laguerre tessellations quite difficult: the generator points and radius marks have to be modelled simultaneously. This may imply that the reconstruction methods are more efficient than point-process modelling if only samples of similar Laguerre tessellations are needed. We also found that literature recipes for bandwidth choice for estimating correlation functions should be used with care.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
<a href="/en/project/GA19-04412S" target="_blank" >GA19-04412S: New approaches to modeling and statistics of random sets</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Australian and New Zealand Journal of Statistics
ISSN
1369-1473
e-ISSN
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Volume of the periodical
63
Issue of the periodical within the volume
1
Country of publishing house
AU - AUSTRALIA
Number of pages
14
Pages from-to
19-32
UT code for WoS article
000675256700003
EID of the result in the Scopus database
2-s2.0-85110577793