BibTeX
@ARTICLE{
         Sengupta2016GbM,
       author = "Biswa Sengupta and Karl J. Friston and Will D. Penny",
       title = "Gradient-based {MCMC} samplers for dynamic causal modelling",
       journal = "NeuroImage",
       volume = "125",
       pages = "1107--1118",
       year = "2016",
       issn = "1053-8119",
       doi = "10.1016/j.neuroimage.2015.07.043",
       url = "http://www.sciencedirect.com/science/article/pii/S1053811915006540",
       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 (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.",
       ad_area = "Neuroscience",
       ad_tools = "ADiMat"
}