Inference in complex systems using multi-phase MCMC sampling with gradient matching burn-in

Statistical inference in nonlinear differential equations (DE) is challenging. The log-likelihood landscape is typically multimodal and every parameter adaptation, e.g. in an MCMC simulation, requires a computationally expensive numerical integration of the DEs. Using numerical methods to solve the equations results in prohibitive computational cost; particularly when one adopts a Bayesian approach in sampling parameters from a posterior distribution. Alternatively, one can try to reduce this computational complexity by obtaining an interpolant to the data from which one can obtain a comparative objective function that matches the gradients of the interpolant and the DEs. By sampling on this cheap representative likelihood surface, bias is introduced to the modelling problem. Current research focuses on reducing this bias by introducing a regularising feedback mechanism from the DEs back to the interpolation scheme (e.g. Niu et al. 2016). The idea is to make the interpolant maximally consistent with the DEs. Although this paradigm has proved to improve performance over näıve gradient matching, the feedback loop fails to fully eradicate bias in the final estimate.