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Spatio-temporal modelling – with a view to biological growth. (English) Zbl 1122.62080

Finkenstädt, Bärbel (ed.) et al., Statistical methods for spatio-temporal systems. Selected invited papers based on the presentations at the 6th séminaire Européen de statistique SemStat held as a summer school of the European Mathematical Society (EMS), Bernried, Germany, December 12–18, 2004. Boca Raton, FL: Chapman & Hall/CRC (ISBN 1-58488-593-9/hbk). Monographs on Statistics and Applied Probability 107, 47-75 (2007).
From the introduction: Modelling of biological growth patterns is a field of mathematical biology that has attracted much attention in recent years, see e.g., M. A. J. Chaplain et al. [On growth and form. Spatio-temporal pattern formation in biology. (1999; Zbl 0932.92006)]. The biological systems modelled are diverse and comprise growth of plant populations, year rings of trees, capillary networks, bacteria colonies, and tumours. This chapter deals with spatio-temporal models for such random growing objects, using spatio-temporal point processes or the theory of Lévy bases. For both types of models, the Poisson process will play a key role, either as a reference process or more directly in the model construction.
For the entire collection see [Zbl 1099.62500].

MSC:

62M30 Inference from spatial processes
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60G51 Processes with independent increments; Lévy processes
62P10 Applications of statistics to biology and medical sciences; meta analysis

Citations:

Zbl 0932.92006
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