4.6 Article

Bayesian inference of a non-local proliferation model

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Summary: This paper investigates the EBT algorithm (a particle method) for the nonlocal equation with a discontinuous interaction kernel. The main challenge lies in the low regularity of the kernel, which prevents the use of standard arguments. Instead, the radial symmetry of the problem is utilized and transformed using spherical coordinates. The resulting equation has a Lipschitz kernel with a singularity at zero. A new weighted flat norm is introduced, and the convergence of the particle method is proved in this norm. The two-dimensional case is also discussed, which requires the application of the theory of measure spaces on general metric spaces, and numerical simulations are provided to support the theoretical results.

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