Abstract
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. Fully Bayesian inference for state-space SDEMEMs is performed, 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. 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 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. The methodology is demonstrated on three case studies, including tumor growth dynamics and neuronal data. The gains in terms of increased computational efficiency are model and data dependent, but unless bespoke sampling strategies requiring analytical derivations are possible for a given model, we generally observe an efficiency increase of one order of magnitude when using correlated particle methods together with our blocked-Gibbs strategy.
Highlights
Stochastic differential equations (SDEs) are arguably the most used and studied stochastic dynamic models
While stochastic differential equation mixed-effects model (SDEMEM) are a flexible class of models for ‘‘population estimation’’, their use has been limited by technical difficulties that make the execution of inference algorithms computationally intensive
Our work proposed strategies to both (i) produce Bayesian inference for very general SDEMEMs, without the limitations of previous methods; (ii) alleviate the computational requirements induced by the generality of our methods
Summary
Stochastic differential equations (SDEs) are arguably the most used and studied stochastic dynamic models. The Bayesian literature offers powerful solutions to the inference problem, when observations arise from state-space models Our goal is to produce novel Gibbs samplers embedding special types of pseudo-marginal algorithms allowing for exact Bayesian inference in a specific class of state-space SDE models. We consider ‘‘repeated measurement experiments’’, modeled via mixed-effects, where the dynamics are Markov processes expressed via stochastic differential equations. Julia and R codes can be found at https://github.com/SamuelWiqvist/efficient_SDEMEM
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