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1.
Neuroimage ; : 116734, 2020 Mar 14.
Artigo em Inglês | MEDLINE | ID: mdl-32179105

RESUMO

This technical note presents a dynamic causal modelling (DCM) procedure for evaluating different models of neurovascular coupling in the human brain - using combined electromagnetic (M/EEG) and functional magnetic resonance imaging (fMRI) data. This procedure compares the evidence for biologically informed models of neurovascular coupling using Bayesian model comparison. First, fMRI data are used to localise regionally specific neuronal responses. The coordinates of these responses are then used as the location priors in a DCM of electrophysiological responses elicited by the same paradigm. The ensuing estimates of model parameters are then used to generate neuronal drive functions, which model pre- or post-synaptic activity for each experimental condition. These functions form the input to a model of neurovascular coupling, whose parameters are estimated from the fMRI data. Crucially, this enables one to evaluate different models of neurovascular coupling, using Bayesian model comparison - asking, for example, whether instantaneous or delayed, pre- or post-synaptic signals mediate haemodynamic responses. We provide an illustrative application of the procedure using a single-subject auditory fMRI and MEG dataset. The code and exemplar data accompanying this technical note are available through the statistical parametric mapping (SPM) software.

2.
Neuroimage ; 211: 116595, 2020 May 01.
Artigo em Inglês | MEDLINE | ID: mdl-32027965

RESUMO

This paper asks whether integrating multimodal EEG and fMRI data offers a better characterisation of functional brain architectures than either modality alone. This evaluation rests upon a dynamic causal model that generates both EEG and fMRI data from the same neuronal dynamics. We introduce the use of Bayesian fusion to provide informative (empirical) neuronal priors - derived from dynamic causal modelling (DCM) of EEG data - for subsequent DCM of fMRI data. To illustrate this procedure, we generated synthetic EEG and fMRI timeseries for a mismatch negativity (or auditory oddball) paradigm, using biologically plausible model parameters (i.e., posterior expectations from a DCM of empirical, open access, EEG data). Using model inversion, we found that Bayesian fusion provided a substantial improvement in marginal likelihood or model evidence, indicating a more efficient estimation of model parameters, in relation to inverting fMRI data alone. We quantified the benefits of multimodal fusion with the information gain pertaining to neuronal and haemodynamic parameters - as measured by the Kullback-Leibler divergence between their prior and posterior densities. Remarkably, this analysis suggested that EEG data can improve estimates of haemodynamic parameters; thereby furnishing proof-of-principle that Bayesian fusion of EEG and fMRI is necessary to resolve conditional dependencies between neuronal and haemodynamic estimators. These results suggest that Bayesian fusion may offer a useful approach that exploits the complementary temporal (EEG) and spatial (fMRI) precision of different data modalities. We envisage the procedure could be applied to any multimodal dataset that can be explained by a DCM with a common neuronal parameterisation.

3.
Cereb Cortex ; 2020 Feb 21.
Artigo em Inglês | MEDLINE | ID: mdl-32083297

RESUMO

Choosing actions that result in advantageous outcomes is a fundamental function of nervous systems. All computational decision-making models contain a mechanism that controls the variability of (or confidence in) action selection, but its neural implementation is unclear-especially in humans. We investigated this mechanism using two influential decision-making frameworks: active inference (AI) and reinforcement learning (RL). In AI, the precision (inverse variance) of beliefs about policies controls action selection variability-similar to decision 'noise' parameters in RL-and is thought to be encoded by striatal dopamine signaling. We tested this hypothesis by administering a 'go/no-go' task to 75 healthy participants, and measuring striatal dopamine 2/3 receptor (D2/3R) availability in a subset (n = 25) using [11C]-(+)-PHNO positron emission tomography. In behavioral model comparison, RL performed best across the whole group but AI performed best in participants performing above chance levels. Limbic striatal D2/3R availability had linear relationships with AI policy precision (P = 0.029) as well as with RL irreducible decision 'noise' (P = 0.020), and this relationship with D2/3R availability was confirmed with a 'decision stochasticity' factor that aggregated across both models (P = 0.0006). These findings are consistent with occupancy of inhibitory striatal D2/3Rs decreasing the variability of action selection in humans.

4.
Behav Brain Res ; 380: 112421, 2020 Feb 17.
Artigo em Inglês | MEDLINE | ID: mdl-31830495

RESUMO

This paper offers a formal account of emotional inference and stress-related behaviour, using the notion of active inference. We formulate responses to stressful scenarios in terms of Bayesian belief-updating and subsequent policy selection; namely, planning as (active) inference. Using a minimal model of how creatures or subjects account for their sensations (and subsequent action), we deconstruct the sequences of belief updating and behaviour that underwrite stress-related responses - and simulate the aberrant responses of the sort seen in post-traumatic stress disorder (PTSD). Crucially, the model used for belief-updating generates predictions in multiple (exteroceptive, proprioceptive and interoceptive) modalities, to provide an integrated account of evidence accumulation and multimodal integration that has consequences for both motor and autonomic responses. The ensuing phenomenology speaks to many constructs in the ecological and clinical literature on stress, which we unpack with reference to simulated inference processes and accompanying neuronal responses. A key insight afforded by this formal approach rests on the trade-off between the epistemic affordance of certain cues (that resolve uncertainty about states of affairs in the environment) and the consequences of epistemic foraging (that may be in conflict with the instrumental or pragmatic value of 'fleeing' or 'freezing'). Starting from first principles, we show how this trade-off is nuanced by prior (subpersonal) beliefs about the outcomes of behaviour - beliefs that, when held with unduly high precision, can lead to (Bayes optimal) responses that closely resemble PTSD.

5.
Neuroimage ; 208: 116452, 2020 Mar.
Artigo em Inglês | MEDLINE | ID: mdl-31830589

RESUMO

Models of coupled phase oscillators are used to describe a wide variety of phenomena in neuroimaging. These models typically rest on the premise that oscillator dynamics do not evolve beyond their respective limit cycles, and hence that interactions can be described purely in terms of phase differences. Whilst mathematically convenient, the restrictive nature of phase-only models can limit their explanatory power. We therefore propose a generalisation of dynamic causal modelling that incorporates both phase and amplitude. This allows for the separate quantifications of phase and amplitude contributions to the connectivity between neural regions. We show, using model-generated data and simulations of coupled pendula, that phase-amplitude models can describe strongly coupled systems more effectively than their phase-only counterparts. We relate our findings to four metrics commonly used in neuroimaging: the Kuramoto order parameter, cross-correlation, phase-lag index, and spectral entropy. We find that, with the exception of spectral entropy, the phase-amplitude model is able to capture all metrics more effectively than the phase-only model. We then demonstrate, using local field potential recordings in rodents and functional magnetic resonance imaging in macaque monkeys, that amplitudes in oscillator models play an important role in describing neural dynamics in anaesthetised brain states.

6.
Neuroimage ; 207: 116453, 2020 Feb 15.
Artigo em Inglês | MEDLINE | ID: mdl-31821868

RESUMO

Metastability is a key source of itinerant dynamics in the brain; namely, spontaneous spatiotemporal reorganization of neuronal activity. This itinerancy has been the focus of numerous dynamic functional connectivity (DFC) analyses - developed to characterize the formation and dissolution of distributed functional patterns over time, using resting state fMRI. However, aside from technical and practical controversies, these approaches cannot recover the neuronal mechanisms that underwrite itinerant (e.g., metastable) dynamics-due to their descriptive, model-free nature. We argue that effective connectivity (EC) analyses are more apt for investigating the neuronal basis of metastability. To this end, we appeal to biologically-grounded models (i.e., dynamic causal modelling, DCM) and dynamical systems theory (i.e., heteroclinic sequential dynamics) to create a probabilistic, generative model of haemodynamic fluctuations. This model generates trajectories in the parametric space of EC modes (i.e., states of connectivity) that characterize functional brain architectures. In brief, it extends an established spectral DCM, to generate functional connectivity data features that change over time. This foundational paper tries to establish the model's face validity by simulating non-stationary fMRI time series and recovering key model parameters (i.e., transition probabilities among connectivity states and the parametric nature of these states) using variational Bayes. These data are further characterized using Bayesian model comparison (within and between subjects). Finally, we consider practical issues that attend applications and extensions of this scheme. Importantly, the scheme operates within a generic Bayesian framework - that can be adapted to study metastability and itinerant dynamics in any non-stationary time series.

7.
Hum Brain Mapp ; 41(4): 928-942, 2020 Mar.
Artigo em Inglês | MEDLINE | ID: mdl-31692192

RESUMO

The moment-to-moment focus of our mind's eye results from a complex interplay of voluntary and involuntary influences on attention. Previous neuroimaging studies suggest that the brain networks of voluntary versus involuntary attention can be segregated into a frontal-versus-parietal or a dorsal-versus-ventral partition-although recent work suggests that the dorsal network may be involved in both bottom-up and top-down attention. Research with nonhuman primates has provided evidence that a key distinction between top-down and bottom-up attention may be the direction of connectivity between frontal and parietal areas. Whereas typical fMRI connectivity analyses cannot disambiguate the direction of connections, dynamic causal modeling (DCM) can model directionality. Using DCM, we provide new evidence that directed connections within the dorsal attention network are differentially modulated for voluntary versus involuntary attention. These results suggest that the intraparietal sulcus exerts a baseline inhibitory effect on the frontal eye fields that is strengthened during exogenous orienting and attenuated during endogenous orienting. Furthermore, the attenuation from endogenous attention occurs even with salient peripheral cues when those cues are known to be counter predictive. Thus, directed connectivity between frontal and parietal regions of the dorsal attention network is highly influenced by the type of attention that is engaged.

8.
Schizophr Bull ; 46(2): 345-353, 2020 Feb 26.
Artigo em Inglês | MEDLINE | ID: mdl-31219602

RESUMO

The dysconnection hypothesis of schizophrenia (SZ) proposes that psychosis is best understood in terms of aberrant connectivity. Specifically, it suggests that dysconnectivity arises through aberrant synaptic modulation associated with deficits in GABAergic inhibition, excitation-inhibition balance and disturbances of high-frequency oscillations. Using a computational model combined with a graded-difficulty visual orientation discrimination paradigm, we demonstrate that, in SZ, perceptual performance is determined by the balance of excitation-inhibition in superficial cortical layers. Twenty-eight individuals with a DSM-IV diagnosis of SZ, and 30 age- and gender-matched healthy controls participated in a psychophysics orientation discrimination task, a visual grating magnetoencephalography (MEG) recording, and a magnetic resonance spectroscopy (MRS) scan for GABA. Using a neurophysiologically informed model, we quantified group differences in GABA, gamma measures, and the predictive validity of model parameters for orientation discrimination in the SZ group. MEG visual gamma frequency was reduced in SZ, with lower peak frequency associated with more severe negative symptoms. Orientation discrimination performance was impaired in SZ. Dynamic causal modeling of the MEG data showed that local synaptic connections were reduced in SZ and local inhibition correlated negatively with the severity of negative symptoms. The effective connectivity between inhibitory interneurons and superficial pyramidal cells predicted orientation discrimination performance within the SZ group; consistent with graded, behaviorally relevant, disease-related changes in local GABAergic connections. Occipital GABA levels were significantly reduced in SZ but did not predict behavioral performance or oscillatory measures. These findings endorse the importance, and behavioral relevance, of GABAergic synaptic disconnection in schizophrenia that underwrites excitation-inhibition balance.

9.
PLoS Biol ; 17(10): e3000426, 2019 10.
Artigo em Inglês | MEDLINE | ID: mdl-31581195

RESUMO

Predictive processing (e.g., predictive coding) is a predominant paradigm in cognitive neuroscience. This Primer considers the various levels of commitment neuroscientists have to the neuronal process theories that accompany the principles of predictive processing. Specifically, it reviews and contextualises a recent PLOS Biology study of alpha oscillations and travelling waves. We will see that alpha oscillations emerge naturally under the computational architectures implied by predictive coding-and may tell us something profound about recurrent message passing in brain hierarchies. Specifically, the bidirectional nature of forward and backward waves speaks to opportunities to understand attention and how it nuances bottom-up and top-down influences.

10.
PLoS Comput Biol ; 15(10): e1007366, 2019 Oct.
Artigo em Inglês | MEDLINE | ID: mdl-31577793

RESUMO

[This corrects the article DOI: 10.1371/journal.pcbi.1005769.].

11.
Cogn Neurosci ; : 1-10, 2019 Oct 16.
Artigo em Inglês | MEDLINE | ID: mdl-31617790

RESUMO

Movement-related theta oscillations in rodent hippocampus coordinate 'forward sweeps' of location-specific neural activity that could be used to evaluate spatial trajectories online. This raises the possibility that increases in human hippocampal theta power accompany the evaluation of upcoming spatial choices. To test this hypothesis, we measured neural oscillations during a spatial planning task that closely resembles a perceptual decision-making paradigm. In this task, participants searched visually for the shortest path between a start and goal location in novel mazes that contained multiple choice points, and were subsequently asked to make a spatial decision at one of those choice points. We observed ~4-8 Hz hippocampal/medial temporal lobe theta power increases specific to sequential planning that were negatively correlated with subsequent decision speed, where decision speed was inversely correlated with choice accuracy. These results implicate the hippocampal theta rhythm in decision tree search during planning in novel environments.

12.
Neurosci Biobehav Rev ; 107: 473-491, 2019 12.
Artigo em Inglês | MEDLINE | ID: mdl-31518636

RESUMO

Emotional awareness (EA) is recognized as clinically relevant to the vulnerability to, and maintenance of, psychiatric disorders. However, the neurocomputational processes that underwrite individual variations remain unclear. In this paper, we describe a deep (active) inference model that reproduces the cognitive-emotional processes and self-report behaviors associated with EA. We then present simulations to illustrate (seven) distinct mechanisms that (either alone or in combination) can produce phenomena - such as somatic misattribution, coarse-grained emotion conceptualization, and constrained reflective capacity - characteristic of low EA. Our simulations suggest that the clinical phenotype of impoverished EA can be reproduced by dissociable computational processes. The possibility that different processes are at work in different individuals suggests that they may benefit from distinct clinical interventions. As active inference makes particular predictions about the underlying neurobiology of such aberrant inference, we also discuss how this type of modelling could be used to design neuroimaging tasks to test predictions and identify which processes operate in different individuals - and provide a principled basis for personalized precision medicine.

13.
Neurosci Conscious ; 2019(1): niz012, 2019.
Artigo em Inglês | MEDLINE | ID: mdl-31528360

RESUMO

Perceptual awareness depends upon the way in which we engage with our sensorium. This notion is central to active inference, a theoretical framework that treats perception and action as inferential processes. This variational perspective on cognition formalizes the notion of perception as hypothesis testing and treats actions as experiments that are designed (in part) to gather evidence for or against alternative hypotheses. The common treatment of perception and action affords a useful interpretation of certain perceptual phenomena whose active component is often not acknowledged. In this article, we start by considering Troxler fading - the dissipation of a peripheral percept during maintenance of fixation, and its recovery during free (saccadic) exploration. This offers an important example of the failure to maintain a percept without actively interrogating a visual scene. We argue that this may be understood in terms of the accumulation of uncertainty about a hypothesized stimulus when free exploration is disrupted by experimental instructions or pathology. Once we take this view, we can generalize the idea of using bodily (oculomotor) action to resolve uncertainty to include the use of mental (attentional) actions for the same purpose. This affords a useful way to think about binocular rivalry paradigms, in which perceptual changes need not be associated with an overt movement.

14.
Biol Cybern ; 113(5-6): 495-513, 2019 12.
Artigo em Inglês | MEDLINE | ID: mdl-31562544

RESUMO

Active inference is an approach to understanding behaviour that rests upon the idea that the brain uses an internal generative model to predict incoming sensory data. The fit between this model and data may be improved in two ways. The brain could optimise probabilistic beliefs about the variables in the generative model (i.e. perceptual inference). Alternatively, by acting on the world, it could change the sensory data, such that they are more consistent with the model. This implies a common objective function (variational free energy) for action and perception that scores the fit between an internal model and the world. We compare two free energy functionals for active inference in the framework of Markov decision processes. One of these is a functional of beliefs (i.e. probability distributions) about states and policies, but a function of observations, while the second is a functional of beliefs about all three. In the former (expected free energy), prior beliefs about outcomes are not part of the generative model (because they are absorbed into the prior over policies). Conversely, in the second (generalised free energy), priors over outcomes become an explicit component of the generative model. When using the free energy function, which is blind to future observations, we equip the generative model with a prior over policies that ensure preferred (i.e. priors over) outcomes are realised. In other words, if we expect to encounter a particular kind of outcome, this lends plausibility to those policies for which this outcome is a consequence. In addition, this formulation ensures that selected policies minimise uncertainty about future outcomes by minimising the free energy expected in the future. When using the free energy functional-that effectively treats future observations as hidden states-we show that policies are inferred or selected that realise prior preferences by minimising the free energy of future expectations. Interestingly, the form of posterior beliefs about policies (and associated belief updating) turns out to be identical under both formulations, but the quantities used to compute them are not.

15.
Cereb Cortex ; 2019 Jul 11.
Artigo em Inglês | MEDLINE | ID: mdl-31298270

RESUMO

The prefrontal cortex is vital for a range of cognitive processes, including working memory, attention, and decision-making. Notably, its absence impairs the performance of tasks requiring the maintenance of information through a delay period. In this paper, we formulate a rodent task-which requires maintenance of delay-period activity-as a Markov decision process and treat optimal task performance as an (active) inference problem. We simulate the behavior of a Bayes optimal mouse presented with 1 of 2 cues that instructs the selection of concurrent visual and auditory targets on a trial-by-trial basis. Formulating inference as message passing, we reproduce features of neuronal coupling within and between prefrontal regions engaged by this task. We focus on the micro-circuitry that underwrites delay-period activity and relate it to functional specialization within the prefrontal cortex in primates. Finally, we simulate the electrophysiological correlates of inference and demonstrate the consequences of lesions to each part of our in silico prefrontal cortex. In brief, this formulation suggests that recurrent excitatory connections-which support persistent neuronal activity-encode beliefs about transition probabilities over time. We argue that attentional modulation can be understood as the contextualization of sensory input by these persistent beliefs.

16.
PLoS Comput Biol ; 15(7): e1007126, 2019 07.
Artigo em Inglês | MEDLINE | ID: mdl-31276488

RESUMO

Living creatures must accurately infer the nature of their environments. They do this despite being confronted by stochastic and context sensitive contingencies-and so must constantly update their beliefs regarding their uncertainty about what might come next. In this work, we examine how we deal with uncertainty that evolves over time. This prospective uncertainty (or imprecision) is referred to as volatility and has previously been linked to noradrenergic signals that originate in the locus coeruleus. Using pupillary dilatation as a measure of central noradrenergic signalling, we tested the hypothesis that changes in pupil diameter reflect inferences humans make about environmental volatility. To do so, we collected pupillometry data from participants presented with a stream of numbers. We generated these numbers from a process with varying degrees of volatility. By measuring pupillary dilatation in response to these stimuli-and simulating the inferences made by an ideal Bayesian observer of the same stimuli-we demonstrate that humans update their beliefs about environmental contingencies in a Bayes optimal way. We show this by comparing general linear (convolution) models that formalised competing hypotheses about the causes of pupillary changes. We found greater evidence for models that included Bayes optimal estimates of volatility than those without. We additionally explore the interaction between different causes of pupil dilation and suggest a quantitative approach to characterising a person's prior beliefs about volatility.


Assuntos
Modelos Biológicos , Pupila/fisiologia , Acetilcolina/fisiologia , Adolescente , Adulto , Teorema de Bayes , Biologia Computacional , Simulação por Computador , Tomada de Decisões , Meio Ambiente , Humanos , Locus Cerúleo/fisiologia , Cadeias de Markov , Modelos Neurológicos , Norepinefrina/fisiologia , Transdução de Sinais , Incerteza , Adulto Jovem
17.
Neuroimage ; 201: 115986, 2019 11 01.
Artigo em Inglês | MEDLINE | ID: mdl-31255808

RESUMO

This technical note describes a variational or Bayesian implementation of representational similarity analysis (RSA) and pattern component modelling (PCM). It considers RSA and PCM as Bayesian model comparison procedures that assess the evidence for stimulus or condition-specific patterns of responses distributed over voxels or channels. On this view, one can use standard variational inference procedures to quantify the contributions of particular patterns to the data, by evaluating second-order parameters or hyperparameters. Crucially, this allows one to use parametric empirical Bayes (PEB) to infer which patterns are consistent among subjects. At the between-subject level, one can then assess the evidence for different (combinations of) hypotheses about condition-specific effects using Bayesian model comparison. Alternatively, one can select a single hypothesis that best explains the pattern of responses using Bayesian model selection. This note rehearses the technical aspects of within and between-subject RSA using a worked example, as implemented in the Statistical Parametric Mapping (SPM) software. En route, we highlight the connection between univariate and multivariate analyses of neuroimaging data and the sorts of analyses that are possible using component modelling and representational similarity analysis.

18.
J Neurosci ; 39(32): 6265-6275, 2019 Aug 07.
Artigo em Inglês | MEDLINE | ID: mdl-31182633

RESUMO

In this paper, we draw from recent theoretical work on active perception, which suggests that the brain makes use of an internal (i.e., generative) model to make inferences about the causes of sensations. This view treats visual sensations as consequent on action (i.e., saccades) and implies that visual percepts must be actively constructed via a sequence of eye movements. Oculomotor control calls on a distributed set of brain sources that includes the dorsal and ventral frontoparietal (attention) networks. We argue that connections from the frontal eye fields to ventral parietal sources represent the mapping from "where", fixation location to information derived from "what" representations in the ventral visual stream. During scene construction, this mapping must be learned, putatively through changes in the effective connectivity of these synapses. Here, we test the hypothesis that the coupling between the dorsal frontal cortex and the right temporoparietal cortex is modulated during saccadic interrogation of a simple visual scene. Using dynamic causal modeling for magnetoencephalography with (male and female) human participants, we assess the evidence for changes in effective connectivity by comparing models that allow for this modulation with models that do not. We find strong evidence for modulation of connections between the two attention networks; namely, a disinhibition of the ventral network by its dorsal counterpart.SIGNIFICANCE STATEMENT This work draws from recent theoretical accounts of active vision and provides empirical evidence for changes in synaptic efficacy consistent with these computational models. In brief, we used magnetoencephalography in combination with eye-tracking to assess the neural correlates of a form of short-term memory during a dot cancellation task. Using dynamic causal modeling to quantify changes in effective connectivity, we found evidence that the coupling between the dorsal and ventral attention networks changed during the saccadic interrogation of a simple visual scene. Intuitively, this is consistent with the idea that these neuronal connections may encode beliefs about "what I would see if I looked there", and that this mapping is optimized as new data are obtained with each fixation.

19.
Psychopharmacology (Berl) ; 236(8): 2405-2412, 2019 Aug.
Artigo em Inglês | MEDLINE | ID: mdl-31230144

RESUMO

The nascent field computational psychiatry has undergone exponential growth since its inception. To date, much of the published work has focused on choice behaviors, which are primarily modeled within a reinforcement learning framework. While this initial normative effort represents a milestone in psychiatry research, the reality is that many psychiatric disorders are defined by disturbances in subjective states (e.g., depression, anxiety) and associated beliefs (e.g., dysmorphophobia, paranoid ideation), which are not considered in normative models. In this paper, we present interoceptive inference as a candidate framework for modeling subjective-and associated belief-states in computational psychiatry. We first introduce the notion and significance of modeling subjective states in computational psychiatry. Next, we present the interoceptive inference framework, and in particular focus on the relationship between interoceptive inference (i.e., belief updating) and emotions. Lastly, we will use drug craving as an example of subjective states to demonstrate the feasibility of using interoceptive inference to model the psychopathology of subjective states.


Assuntos
Simulação por Computador , Cultura , Autoavaliação Diagnóstica , Transtornos Mentais/psicologia , Modelos Psicológicos , Psiquiatria/métodos , Comportamento de Escolha , Fissura/fisiologia , Emoções/fisiologia , Feminino , Humanos , Aprendizagem/fisiologia , Masculino , Transtornos Mentais/diagnóstico , Psiquiatria/tendências
20.
Neuroimage ; 200: 12-25, 2019 10 15.
Artigo em Inglês | MEDLINE | ID: mdl-31226492

RESUMO

This paper provides a worked example of using Dynamic Causal Modelling (DCM) and Parametric Empirical Bayes (PEB) to characterise inter-subject variability in neural circuitry (effective connectivity). It steps through an analysis in detail and provides a tutorial style explanation of the underlying theory and assumptions (i.e, priors). The analysis procedure involves specifying a hierarchical model with two or more levels. At the first level, state space models (DCMs) are used to infer the effective connectivity that best explains a subject's neuroimaging timeseries (e.g. fMRI, MEG, EEG). Subject-specific connectivity parameters are then taken to the group level, where they are modelled using a General Linear Model (GLM) that partitions between-subject variability into designed effects and additive random effects. The ensuing (Bayesian) hierarchical model conveys both the estimated connection strengths and their uncertainty (i.e., posterior covariance) from the subject to the group level; enabling hypotheses to be tested about the commonalities and differences across subjects. This approach can also finesse parameter estimation at the subject level, by using the group-level parameters as empirical priors. The preliminary first level (subject specific) DCM for fMRI analysis is covered in a companion paper. Here, we detail group-level analysis procedures that are suitable for use with data from any neuroimaging modality. This paper is accompanied by an example dataset, together with step-by-step instructions demonstrating how to reproduce the analyses.

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