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Parameter estimation for reaction‐diffusion models of biological invasions
Author(s) -
Soubeyrand Samuel,
Roques Lionel
Publication year - 2014
Publication title -
population ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.819
H-Index - 59
eISSN - 1438-390X
pISSN - 1438-3896
DOI - 10.1007/s10144-013-0415-0
Subject(s) - parametric statistics , estimation , estimation theory , mathematics , population , noise (video) , inverse problem , computer science , reaction–diffusion system , partial differential equation , diffusion process , mathematical optimization , stochastic differential equation , parametric model , algorithm , statistics , artificial intelligence , mathematical analysis , engineering , knowledge management , demography , innovation diffusion , sociology , image (mathematics) , systems engineering
In this note, we discuss parameter estimation for population models based on partial differential equations (PDEs). Parametric estimation is first considered in the perspective of inverse problems (i.e., when the observation of the solution of a PDE is exactly observed or noise‐free). Then, adopting the point of view of statistics, we turn to parametric estimation for PDEs using more realistic noisy measurements. The approach that we describe uses mechanistic‐statistical models which combine (1) a PDE‐based submodel describing the dynamic under study and (2) a stochastic submodel describing the observation process. This Note is expected to contribute to bridge the gap between modelers using PDEs and population ecologists collecting and analyzing spatio‐temporal data.