Particle Methods for Stochastic Differential Equation Mixed Effects Models
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Parameter inference for stochastic differential equation mixed effects models (SDEMEMs) is a challenging problem. Analytical solutions for these models are rarely available, which means that the likelihood is also intractable. In this case, exact inference is possible using the pseudo-marginal approach, where the intractable likelihood is replaced with a nonnegative unbiased estimate. A useful application of this idea is particle MCMC, which uses a particle filter estimate of the likelihood. While the exact posterior is targeted by these methods, a naive implementation for SDEMEMs can be highly inefficient. We develop three extensions to the naive approach which exploits specific aspects of SDEMEMs and other advances such as correlated pseudo-marginal methods. We compare these methods on real and simulated data from a tumour xenography study on mice.
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