Dynamic causal modeling: Difference between revisions

Revision as of 09:10, 14 September 2018

Revision as of 15:43, 18 October 2018

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\end{align}</math>

The first equality describes the change in neural activity <math>z</math> with respect to time (i.e. <math>\dot{z}</math>), which cannot be directly observed using non-invasive functional imaging modalities. The evolution of neural activity over time is controlled by a neural function <math>f</math> with parameters <math>\theta^{(n)}</math> and experimental inputs <math>u</math>. The neural activity in turn causes the timeseries <math>y</math> (second equality), which are generated via aan observation function <math>g</math> with parameters <math>\theta^{(h)}</math>. Additive observation noise <math>\epsilon</math> completes the observation model. Usually, the neural parameters <math>\theta^{(n)}</math> are of key interest, which for example represent connection strengths that may change under different experimental conditions.

Specifying a DCM requires selecting a neural model <math>f</math> and observation model <math>g</math> and setting appropriate [[Prior probability|priors]] over the parameters; e.g. selecting which connections should be switched on or off.

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DCM is a hypothesis-driven approach for investigating the interactions among pre-defined regions of interest. It is not ideally suited for exploratory analyses<ref name=":0" />. Although methods have been implemented for automatically searching over reduced models ([[Bayesian model reduction|Bayesian Model Reduction]]) and for modelling large-scale brain networks<ref name=":4" />, these methods require an explicit specification of model space. In neuroimaging, approaches such as [[Psychophysiological Interaction|psychophysiological interaction (PPI)]] analysis may be more appropriate for exploratory use; especially for discovering key nodes for subsequent DCM analysis.

The variational Bayesian methods used for model estimation in DCM are based on the on the Laplace assumption, which treats the posterior over parameters as Gaussian. This approximation can fail in the context of highly non-linear models, where local minima may preclude the free energy from serving as a tight bound on log model evidence. Sampling approaches provide the gold standard; however, they are time consuming and have typically been used to validate the variational approximations in DCM<ref>{{Cite journal|last=Chumbley|first=Justin R.|last2=Friston|first2=Karl J.|last3=Fearn|first3=Tom|last4=Kiebel|first4=Stefan J.|date=2007-11|title=A Metropolis–Hastings algorithm for dynamic causal models|journal=NeuroImage|volume=38|issue=3|pages=478–487|doi=10.1016/j.neuroimage.2007.07.028|pmid=17884582|issn=1053-8119}}</ref>.

== Software implementations ==