Efficient inference for stochastic differential equation mixed-effects models using correlated particle pseudo-marginal algorithms
Journal article, 2021

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.

state-space model

Bayesian inference

sequential Monte Carlo

random effects


Samuel Wiqvist

Lund University

Andrew Golightly

Newcastle University

Ashleigh T. McLean

Newcastle University

Umberto Picchini

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Computational Statistics and Data Analysis

0167-9473 (ISSN)

Vol. 157 107151

Deep learning and likelihood-free Bayesian inference for stochastic modelling

Swedish Research Council (VR), 2020-01-01 -- 2023-12-31.

Chalmers AI Research Centre (CHAIR), 2020-01-01 -- 2024-12-31.

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Control Engineering



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