Parameter inference for stochastic differential equation mixed effects models (SDEMEMs) is challenging. Analytical solutions for these models are rarely available, which means that the likelihood is also intractable. In this case, exact inference (up to the discretisation of the stochastic differential equation) is possible using particle MCMC methods. Although the exact posterior is targeted by these methods, a naive implementation for SDEMEMs can be highly inefficient. Our article develops three extensions to the naive approach which exploit specific aspects of SDEMEMs and other advances such as correlated pseudo-marginal methods. We compare these methods on simulated data and data from a tumour xenography study on mice.
We thank Umberto Picchini and the research team at the Centre for Nanomedicine and Theranostics (DTU Nanotech, Denmark) for providing the real data and Andrew Golightly for useful feedback on an earlier draft of this paper. IB was supported by an Australian Reseach Training Program Stipend and an ACEMS Top-Up Scholarship. IB would also like to thank ACEMS for funding a trip to visit RK at UNSW where some of this research took place. CD was supported by an Australian Research Council Discovery Project (DP200102101). The work by RK was partially supported by an ARC Center of Excellence grant (CE140100049). We gratefully acknowledge the computational resources provided by QUT’s High Performance Computing and Research Support Group (HPC).
"Particle Methods for Stochastic Differential Equation Mixed Effects Models." Bayesian Anal. 16 (2) 575 - 609, June 2021. https://doi.org/10.1214/20-BA1216