Abstract

Co-authors: Paul Kirk (Imperial College London), Angelique Ale (Imperial College London), Ann Babtie (Imperial College London), Sarah Filippi (Imperial College London), Eszter Lakatos (Imperial College London), Daniel Silk (Imperial College London), Thomas Thorn (University of Edinburgh)

We consider approximate Bayesian computation (ABC) approaches to model the dynamics and evolution of molecular networks. Initially conceived to cope with problems with intractable likelihoods, ABC has gained popularity over the past decade. But there are still considerable problems in applying ABC to real-world problems, some of which are shared with exact Bayesian inference, but some are due to the nature of ABC . Here we will present some recent advances that allow us to apply ABC sequential Monte Carlo (SMC) to real biological problems. The rate of convergence of ABC -SMC depends crucially on the schedule of thresholds, ?t, t=1,2,,T, and the perturbation kernels used to generate proposals from the previous population of parameters. We show how both of these can be tuned individually, and jointly. Careful calibration of the ABC -SMC approach can result in a 10-fold reduction in the computational burden (or more). I will also provide an overview of an alternative approach where, rather than approximating the likelihood in an ABC framework, we provide approximations to the master equation that describes the evolution of the stochastic system, that go beyond the conventional linear noise approximation (LNA). This allows us to tackle systems with ``interesting dynamics”, that are typically beyond the scope of the LNA , and we will show how to use such approaches in exact Bayesian inference procedures (including nested sampling and SMC ).