Gaussian process enhanced semi-automatic approximate Bayesian computation: parameter inference in a stochastic differential equation system for chemotaxis

Chemotaxis is a type of cell movement in response to chemical stimulus which plays key role multiple biophysical processes, such as embryogenesis and wound healing, crucial for understanding metastasis cancer research. In the literature, chemotaxis has been modelled using models based on systems nonlinear stochastic partial differential equations (NSPDEs), are known be challenging statistical inference due intractability associated likelihood high computational costs their numerical integration. Therefore, data analysis this context limited comparing predictions from NSPDE laboratory simple descriptive statistics. We present statistically rigorous framework parameter estimation complex described by NSPDEs one chemotaxis. adopt likelihood-free approach approximate Bayesian computations with sequential Monte Carlo (ABC-SMC) allows circumventing likelihood. To find informative summary statistics, performance ABC, we propose use Gaussian process (GP) regression model. The interpolation provided GP turns out useful its own merits: it relatively accurately estimates parameters model uncertainty quantification, at very low cost. Our proposed methodology considerable part completed before having observed any data, providing practical toolbox experimental scientists whose modes operation frequently involve experiments taking place distinct points time. an application externally synthetic demonstrate that correction ABC-SMC essential accurate some more flexible quantification.