Title: Bayesian parameter identification in Cahn-Hilliard models for biological growth,
Abstract: We consider the inverse problem of parameter estimation in a diffuse
interface model for tumour growth. The model consists of a fourth-order
Cahn--Hilliard system and contains three phenomenological parameters: the
tumour proliferation rate, the nutrient consumption rate, and the chemotactic
sensitivity. We study the inverse problem within the Bayesian framework and
construct the likelihood and noise for two typical observation settings. One
setting involves an infinite-dimensional data space where we observe the full
tumour. In the second setting we observe only the tumour volume, hence the data
space is finite-dimensional. We show the well-posedness of the posterior
measure for both settings, building upon and improving the analytical results
in [C. Kahle and K.F. Lam, Appl. Math. Optim. (2018)]. A numerical example
involving synthetic data is presented in which the posterior measure is
numerically approximated by the Sequential Monte Carlo approach with tempering.