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== Motivation ==
DCM was developed for (and is applied principally to) estimating coupling among brain regions and how that coupling is influenced by experimental changes (e.g., time or context). The basic idea is to construct reasonably realistic models of interacting
DCM is used to infer the causal architecture of coupled nonlinear dynamical systems, by specifying models of how the data were generated and comparing the [[Marginal likelihood|evidence]] for different models. Dynamic Causal Models (DCMs) are nonlinear state-space models in continuous time that model the dynamics of hidden states in the nodes of a probabilistic graphical model, where conditional dependencies are parameterised in terms of directed effective connectivity. Unlike [[Bayesian network|Bayesian Networks]] the networks used in DCM can be cyclic, and unlike [[Structural equation modeling|Structural Equation modelling]] and [[Granger causality]], DCM does not depend on the theory of Martingales, i.e., it does not assume that random fluctuations' are serially uncorrelated.▼
== Procedure ==
▲DCM was developed for (and applied principally to) estimating coupling among brain regions and how that coupling is influenced by experimental changes (e.g., time or context). The basic idea is to construct reasonably realistic models of interacting (cortical) regions or nodes. These models are then supplemented with a forward model of how the hidden states of each node (e.g., neuronal activity) map to measured responses. This enables the best model and its parameters (i.e., effective connectivity) to be identified from observed data. [[Bayesian model comparison]] is used to select the best model in terms of its evidence, which can then be characterised in terms of its parameters. This enables one to test hypotheses about how nodes communicate; e.g., whether activity in a given neuronal population modulates the coupling between other populations, in a task-specific fashion.
DCM studies typically involve the following stages:
# Formulating hypotheses and conducting an experiment to test those hypotheses.
# Preparing the acquired data for modelling (such as selecting relevant data features and removing confounds from the data).
# Specifying one or more models (DCMs) of how the data were caused.
# Comparing the evidence for these models, or taking the evidence or parameters to the group level for testing hypotheses.
▲
In functional neuroimaging, the data may be functional magnetic resonance imaging (fMRI) measurements or electrophysiological (e.g., in magnetoencephalography or electroencephalography; MEG/EEG). Brain responses are evoked by known deterministic inputs (experimentally controlled stimuli) that embody designed changes in sensory stimulation or cognitive set. These experimental or exogenous variables can change hidden states in one of two ways. First, they can elicit responses through direct influences on specific network nodes. This would be appropriate, for example, in modelling sensory evoked responses in the early visual cortex. The second class of inputs exerts their effects vicariously, through a modulation of the coupling among nodes, for example, the influence of attention on the processing of sensory information. The hidden states cover any neurophysiological or biophysical variables needed to form observed outputs. These outputs are measured (hemodynamic or electromagnetic) responses over the sensors considered. Bayesian inversion furnishes the marginal likelihood (evidence) of the model and the posterior distribution of its parameters (e.g., neuronal coupling strengths). The evidence is used for Bayesian model selection (BMS) to disambiguate between competing models, while the posterior distribution of the parameters is used to characterise the model selected.
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