Bayesian Parameter Inference for Stochastic Differential Equation Mixed Effects Models

Abstract:

Parameter inference for stochastic differential equation mixed effects models (SDEMEMs) is a challenging problem. Analytical solutions for these models are rarely available, which means thatthe likelihood is also intractable.  Andrieu et al. (2009) proved that exact inference is possible for state space models with intractable likelihoods, provided the transition density can be simulated from. These pseudo-marginal methods replace the intractable likelihood with a nonnegative unbiased estimate, calculated with the use of auxiliary variables. A useful application of this idea is particle MCMC, where the unbiased estimate is supplied by a particle filter.  While the exactposterior is targetted by these methods, a naive implementation for SDEMEMs can be highly inefficient. We present 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 to data from a tumour xenography study on mice.  This is joint work with Chris Drovandi and Robert Kohn.