Efficient inference for stochastic differential equation mixed-effects models using correlated particle pseudo-marginal algorithms

Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that are able to account for random variability inherent in the underlying time-dynamics, as well as the variability between experimental units and, optionally, account for measurement error. We perform fully Bayesian inference for state-space SDEMEMs, using data at discrete times that may be incomplete and subject to measurement error. However, the inference problem is complicated by the typical intractability of the observed data likelihood which motivates the use of sampling-based approaches such as Markov chain Monte Carlo. Our proposed approach is the use of a Gibbs sampler to target the marginal posterior of all parameter values of interest. Our algorithm is made computationally efficient through careful use of blocking strategies and correlated pseudo-marginal Metropolis-Hastings steps within the Gibbs scheme. The resulting methodology is flexible and is able to deal with a large class of SDEMEMs. We demonstrate the methodology on three case studies, including tumor growth dynamics and neuronal data. For these three applications, we found that our algorithm is up to 40 times more efficient, depending on the considered application, than similar algorithms not using correlated particle filters.