TY  - JOUR
A1  - Hellmuth, Kathrin
A1  - Klingenberg, Christian
A1  - Li, Qin
A1  - Tang, Min
T1  - Multiscale convergence of the inverse problem for chemotaxis in the Bayesian setting
T2  - Computation
N2  - Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe the phenomenon are the celebrated Keller–Segel equation and a chemotaxis kinetic equation. These two equations describe the organism's movement at the macro- and mesoscopic level, respectively, and are asymptotically equivalent in the parabolic regime. The way in which the organism responds to a chemical stimulus is embedded in the diffusion/advection coefficients of the Keller–Segel equation or the turning kernel of the chemotaxis kinetic equation. Experiments are conducted to measure the time dynamics of the organisms' population level movement when reacting to certain stimulation. From this, one infers the chemotaxis response, which constitutes an inverse problem. In this paper, we discuss the relation between both the macro- and mesoscopic inverse problems, each of which is associated with two different forward models. The discussion is presented in the Bayesian framework, where the posterior distribution of the turning kernel of the organism population is sought. We prove the asymptotic equivalence of the two posterior distributions.
KW  - inverse problems
KW  - Bayesian approach
KW  - kinetic chemotaxis equation
KW  - Keller–Segel model
KW  - multiscale modeling
KW  - asymptotic analysis
KW  - velocity jump process
KW  - mathematical biology
Y1  - 2021
UR  - https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/25021
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-250216
SN  - 2079-3197
VL  - 9
IS  - 11
ER  -