When: 10 february 2021, 13-14
Where: This seminar is given online. E-mail Dan Hedlin if you want to attend.


An important, and well studied, class of stochastic models is given by stochastic differential equations (SDEs). In this talk, we consider inference for SDEs in mixed-effects modelling where measurements from several individuals are jointly fit, to provide inference at the "population level". The advantage of using stochastic differential equation mixed-effects models (SDEMEMs) is that these are flexible hierarchical models that account for (i) the intrinsic random variability in the latent states dynamics, as well as (ii) the variability between individuals, and also (iii) account for measurement error. When modelling real experiments, while the underlying dynamics may be expressed by SDEs, observations may be incomplete (observed at discrete times) and noisy. This gives rise to methodological and computational difficulties and, technically, we are dealing with a state-space model.

Fully Bayesian inference for nonlinear SDEMEMs 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. A Gibbs sampler is proposed to target the marginal posterior of all parameter values of interest. The algorithm is made computationally efficient through careful use of blocking strategies, particle filters (sequential Monte Carlo) and correlated pseudo-marginal approaches. The resulting methodology is flexible, general and is able to deal with a large class of nonlinear SDEMEMs. The methodology is demonstrated on tumour growth dynamics and neuronal data.

This is joint work with Samuel Wiqvist, Andrew Golightly and Ashleigh McLean.