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

Abstract

We perform fully Bayesian inference for stochastic differential equation mixed-effects models (SDEMEMs) using data at discrete times that may be incomplete and subject to measurement error. 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 consider inference for state-space SDEMEMs, 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 state-space models describing two applications of increasing complexity and compare with alternative approaches. For these two applications, we found that our algorithm is about ten to forty times more efficient, depending on the considered application, than similar algorithms not using correlated particle filters.

Bayesian inference for stochastic differential equation mixed effects models

“…To further improve efficiency, we exploit bridge proposals in the particle filter rather than proposing directly from the (approximate) transition density as in the standard bootstrap filter used by Wiqvist et al (2019). By including the IAPM and MPM methods, our paper provides a more comprehensive suite of particle methods for application to general statespace SDEMEMs.…”

“…By including the IAPM and MPM methods, our paper provides a more comprehensive suite of particle methods for application to general statespace SDEMEMs. Wiqvist et al (2019) allow the number of particles to vary between individuals, which is also straightforward to implement in our methods.…”