Parameter inference and model selection
The mathematical models described in the various WPs depend on several biophysical parameters. However parameters cannot be directly measured in the laboratory, or where patient specific variation needs to be accounted for in a drive towards personalised medicine. We face the challenging task to learn (or “infer”) them within the context of the mathematical model itself, based on a systematic comparison of the outputs from computer simulations and experimental observations. In this work package, we will address this problem with state-of-the-art computer-intensive statistical inference
Project 1: parameter optimization in an approximate maximum likelihood sense, or sample them from the posterior distribution with Monto Carlo methods.
Project2: Design of a surrogate objective function using a metric based on a set of carefully selected summary statistics for the stochastic agent-based models.
Project3: systematically comparing variational verse sequential methods of "data assimilation”.
Project4: we will pursue model selection within a sound statistical framework, for example MCMC-based techniques, or lower-order approximations based on the Laplace method or BIC.
Project 5: we will upscale these developed inference methods to account for interactions with the extracellular matrix fibres within tissues, as required in other work packages.
Team: Prof. Husmeier (team leader), Prof. Ogden, Dr. Yin, Prof. Luo, Prof. Berry, Prof. Chaplain, Prof. Insall, Prof. Smith, PDRA4, PhD5