Bayesian Inference on the Keller–Segel Model

Abstract

The Keller–Segel (KS) model is a system of partial differential equations that describe chemotaxis—how cells move in response to chemical stimulus. Simulated data in the form of cell counts are used to carry out Bayesian inference on the ks model. A Bayesian analysis on the ks model is performed on three sets of initial conditions. First, the KS model is solved numerically using a finite difference method and Bayesian inference is performed on parameters of the model such as the cell diffusion and chemical sensitivity. We investigate the predictive posterior distribution of future data and the convergence of the 95% credible interval of cell diffusion at different grid sizes using the three different initial conditions.

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