Multiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Setting

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 describe phenomenon are celebrated Keller–Segel equation chemotaxis kinetic equation. These two equations organism’s at macro- mesoscopic level, respectively, asymptotically equivalent parabolic regime. The way which organism responds stimulus is embedded diffusion/advection coefficients turning kernel Experiments conducted measure time dynamics organisms’ population level when reacting certain stimulation. From this, one infers response, constitutes inverse problem. In this paper, we discuss relation between both problems, each associated with different forward models. discussion presented Bayesian framework, where posterior distribution sought. We prove asymptotic equivalence distributions.