Journal
NEUROIMAGE
Volume 125, Issue -, Pages 1107-1118Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.neuroimage.2015.07.043
Keywords
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Funding
- Wellcome Trust [091593/Z/10/Z]
- EPSRC [EP/I017909/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/I017909/1] Funding Source: researchfish
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In this technical note, we derive two MCMC (Markov chain Monte Carlo) samplers for dynamic causal models (DCMs). Specifically, we use (a) Hamiltonian MCMC (HMC-E) where sampling is simulated using Hamilton's equation of motion and (b) Langevin Monte Carlo algorithm (LMC-R and LMC-E) that simulates the Langevin diffusion of samples using gradients either on a Euclidean (E) or on a Riemannian (R) manifold. While LMC-R requires minimal tuning, the implementation of HMC-E is heavily dependent on its tuning parameters. These parameters are therefore optimised by learning a Gaussian process model of the time-normalised sample correlation matrix. This allows one to formulate an objective function that balances tuning parameter exploration and exploitation, furnishing an intervention-free inference scheme. Using neural mass models (NMMs)-a class of biophysically motivated DCMs-we find that HMC-E is statistically more efficient than LMC-R (with a Riemannian metric); yet both gradient-based samplers are far superior to the random walk Metropolis algorithm, which proves inadequate to steer away from dynamical instability. (C) 2015 The Authors. Published by Elsevier Inc.
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