Particle Methods for Stochastic Differential Equation Mixed Effects Models

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.

Automated summary

Parameter inference for SDEMEM models is challenging due to the lack of analytical solutions and intractable likelihood calculations. Particle MCMC methods offer exact inference possibilities, but naive implementations may be highly inefficient. This article introduces three extensions to improve inference efficiency by exploiting specific aspects of SDEMEM models and incorporating correlated pseudo-marginal methods. Comparisons on simulated and real data from a tumour xenography study demonstrate the effectiveness of these methods.