Abstract
In this technical note, we derive two MCMC (Markov chain Monte Carlo) samplers for dynamic causal models (DCMs). Specifically, we use (a) Hamiltonian MCMC (HMCE) where sampling is simulated using Hamilton's equation of motion and (b) Langevin Monte Carlo algorithm (LMCR and LMCE) that simulates the Langevin diffusion of samples using gradients either on a Euclidean (E) or on a Riemannian (R) manifold. While LMCR requires minimal tuning, the implementation of HMCE is heavily dependent on its tuning parameters. These parameters are therefore optimised by learning a Gaussian process model of the timenormalised sample correlation matrix. This allows one to formulate an objective function that balances tuning parameter exploration and exploitation, furnishing an interventionfree inference scheme. Using neural mass models (NMMs)a class of biophysically motivated DCMswe find that HMCE is statistically more efficient than LMCR (with a Riemannian metric); yet both gradientbased samplers are far superior to the random walk Metropolis algorithm, which proves inadequate to steer away from dynamical instability.
Original language  English 

Pages (fromto)  11071118 
Number of pages  12 
Journal  NeuroImage 
Volume  125 
Early online date  23 Jul 2015 
DOIs  
Publication status  Published  15 Jan 2016 
Keywords
 Algorithms
 Bayes Theorem
 Humans
 ComputerAssisted Image Interpretation
 Markov Chains
 Theoretical Models
 Monte Carlo Method
 Neuroimaging
 Comparative Study
Profiles

William Penny
 School of Psychology  Professor in Psychology
 Centre for Behavioural and Experimental Social Science
Person: Research Group Member, Academic, Teaching & Research