A unified Bayesian inversion approach for a class of tumor growth models with different pressure laws

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In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations.

• The models contain uncertain parameters and are indexed by a physical parameter $m$, which characterizes the constitutive relation between density and pressure.
• Based on these models, we employ the Bayesian inversion framework to infer parametric and nonparametric unknowns that affect tumor growth from noisy observations of tumor cell density.
• We establish the well-posedness and the stability theories for the Bayesian inversion problem and further prove the convergence of the posterior distribution in the so-called incompressible limit, $m \rightarrow \infty$.