Dynamic causal modelling (DCM)¶
Introduction¶
In neuroimaging, DCM is used for investigating effective connectivity  the directed effects of neural populations on one another.
Typically, effective connectivity cannot be directly observed. Rather, it needs to be inferred from downstream consequences, such as fMRI, EEG or MEG recordings. DCM provides the necessary tools to infer the underlying neural connectivity which gave rise to the observed data.
DCM workflow¶

Model specification. For each participant, specify a model that describes how experimental stimuli (or the resting state) generated their neural activity and connectivity, and in turn, their neuroimaging data. These models contain parameters  unknown quantities such as neural connection strengths, which we wish to estimate from the data.

Model estimation (or model inversion). The software will find a setting of the parameters that makes the model as good as possible. Here, the measure of goodness is a statistic called the free energy or evidence lower bound (ELBO), which quantifies the tradeoff between the model’s accuracy and complexity.

Group level modelling. Take all participants’ estimated parameters to the group level and fit a second level model, using an approach called Parametric Empirical Bayes (PEB). This captures the commonalities and differences between participants, and returns a score for the quality of the entire grouplevel model (free energy).

Bayesian model comparison. Compare the free energy of different candidate grouplevel (PEB) models, which differ in terms of which connectivity parameters or covariates are included.

Predictive validity. Optionally, assess the predictive accuracy of the model parameters using crossvalidation, to evaluate whether the detected effects were large enough to be useful.
What’s the technical definition of DCM?
DCM can refer to:
1. Dynamic Causal Modelling, which is a set of mathematical methods for modelling data.
2. Dynamic Causal Model, which is a specific model created using this framework.
3. The software implementation in SPM and other packages.
From a technical perspective, Dynamic Causal Modelling has two key ingredients:
 State space models, which define the dynamics of latent variables (such as neural voltages, conductances), as well as how these latent variables give rise to data.
 Variational Bayes methods, which rapidly score the evidence for candidate models, enabling Bayesian model comparison.