Rosalyn J. Moran

Bayesian model selection for group studies

Bayesian model selection (BMS) is a powerful method for determining the most likely among a set of competing hypotheses about the mechanisms that generated observed data. BMS has recently found widespread application in neuroimaging, particularly in the context of dynamic causal modelling (DCM). However, so far, combining BMS results from several subjects has relied on simple (fixed effects) metrics, e.g. the group Bayes factor (GBF), that do not account for group heterogeneity or outliers. In this paper, we compare the GBF with two random effects methods for BMS at the between-subject or group level. These methods provide inference on model-space using a classical and Bayesian perspective respectively. First, a classical (frequentist) approach uses the log model evidence as a subject-specific summary statistic. This enables one to use analysis of variance to test for differences in log-evidences over models, relative to inter-subject differences. We then consider the same problem in Bayesian terms and describe a novel hierarchical model, which is optimised to furnish a probability density on the models themselves. This new variational Bayes method rests on treating the model as a random variable and estimating the parameters of a Dirichlet distribution which describes the probabilities for all models considered. These probabilities then define a multinomial distribution over model space, allowing one to compute how likely it is that a specific model generated the data of a randomly chosen subject as well as the exceedance probability of one model being more likely than any other model. Using empirical and synthetic data, we show that optimising a conditional density of the model probabilities, given the log-evidences for each model over subjects, is more informative and appropriate than both the GBF and frequentist tests of the log-evidences. In particular, we found that the hierarchical Bayesian approach is considerably more robust than either of the other approaches in the presence of outliers. We expect that this new random effects method will prove useful for a wide range of group studies, not only in the context of DCM, but also for other modelling endeavours, e.g. comparing different source reconstruction methods for EEG/MEG or selecting among competing computational models of learning and decision-making.

Ten simple rules for dynamic causal modeling.

Dynamic causal modeling (DCM) is a generic Bayesian framework for inferring hidden neuronal states from measurements of brain activity. It provides posterior estimates of neurobiologically interpretable quantities such as the effective strength of synaptic connections among neuronal populations and their context-dependent modulation. DCM is increasingly used in the analysis of a wide range of neuroimaging and electrophysiological data. Given the relative complexity of DCM, compared to conventional analysis techniques, a good knowledge of its theoretical foundations is needed to avoid pitfalls in its application and interpretation of results. By providing good practice recommendations for DCM, in the form of ten simple rules, we hope that this article serves as a helpful tutorial for the growing community of DCM users.

Analysing connectivity with Granger causality and dynamic causal modelling

Highlights ► A brief introduction to the analysis of directed connectivity in brain networks. ► An overview of advances in Granger causality and dynamic causal modelling. ► A comparative evaluation of both approaches in terms of their pros and cons.

Connectivity Changes Underlying Spectral EEG Changes during Propofol-Induced Loss of Consciousness

The mechanisms underlying anesthesia-induced loss of consciousness remain a matter of debate. Recent electrophysiological reports suggest that while initial propofol infusion provokes an increase in fast rhythms (from beta to gamma range), slow activity (from delta to alpha range) rises selectively during loss of consciousness. Dynamic causal modeling was used to investigate the neural mechanisms mediating these changes in spectral power in humans. We analyzed source-reconstructed data from frontal and parietal cortices during normal wakefulness, propofol-induced mild sedation, and loss of consciousness. Bayesian model selection revealed that the best model for explaining spectral changes across the three states involved changes in corticothalamic interactions. Compared with wakefulness, mild sedation was accounted for by an increase in thalamic excitability, which did not further increase during loss of consciousness. In contrast, loss of consciousness per se was accompanied by a decrease in backward corticocortical connectivity from frontal to parietal cortices, while thalamocortical connectivity remained unchanged. These results emphasize the importance of recurrent corticocortical communication in the maintenance of consciousness and suggest a direct effect of propofol on cortical dynamics.

Dynamic causal modeling for EEG and MEG

We present a review of dynamic causal modeling (DCM) for magneto‐ and electroencephalography (M/EEG) data. DCM is based on a spatiotemporal model, where the temporal component is formulated in terms of neurobiologically plausible dynamics. Following an intuitive description of the model, we discuss six recent studies, which use DCM to analyze M/EEG and local field potentials. These studies illustrate how DCM can be used to analyze evoked responses (average response in time), induced responses (average response in time‐frequency), and steady‐state responses (average response in frequency). Bayesian model comparison plays a critical role in these analyses, by allowing one to compare equally plausible models in terms of their model evidence. This approach might be very useful in M/EEG research; where correlations among spatial and neuronal model parameter estimates can cause uncertainty about which model best explains the data. Bayesian model comparison resolves these uncertainties in a principled and formal way. We suggest that DCM and Bayesian model comparison provides a useful way to test hypotheses about distributed processing in the brain, using electromagnetic data. Hum Brain Mapp, 2009.

Dopamine, Affordance and Active Inference

The role of dopamine in behaviour and decision-making is often cast in terms of reinforcement learning and optimal decision theory. Here, we present an alternative view that frames the physiology of dopamine in terms of Bayes-optimal behaviour. In this account, dopamine controls the precision or salience of (external or internal) cues that engender action. In other words, dopamine balances bottom-up sensory information and top-down prior beliefs when making hierarchical inferences (predictions) about cues that have affordance. In this paper, we focus on the consequences of changing tonic levels of dopamine firing using simulations of cued sequential movements. Crucially, the predictions driving movements are based upon a hierarchical generative model that infers the context in which movements are made. This means that we can confuse agents by changing the context (order) in which cues are presented. These simulations provide a (Bayes-optimal) model of contextual uncertainty and set switching that can be quantified in terms of behavioural and electrophysiological responses. Furthermore, one can simulate dopaminergic lesions (by changing the precision of prediction errors) to produce pathological behaviours that are reminiscent of those seen in neurological disorders such as Parkinsons disease. We use these simulations to demonstrate how a single functional role for dopamine at the synaptic level can manifest in different ways at the behavioural level.

A neural mass model of spectral responses in electrophysiology

We present a neural mass model of steady-state membrane potentials measured with local field potentials or electroencephalography in the frequency domain. This model is an extended version of previous dynamic causal models for investigating event-related potentials in the time-domain. In this paper, we augment the previous formulation with parameters that mediate spike-rate adaptation and recurrent intrinsic inhibitory connections. We then use linear systems analysis to show how the models spectral response changes with its neurophysiological parameters. We demonstrate that much of the interesting behaviour depends on the non-linearity which couples mean membrane potential to mean spiking rate. This non-linearity is analogous, at the population level, to the firing rate–input curves often used to characterize single-cell responses. This function depends on the models gain and adaptation currents which, neurobiologically, are influenced by the activity of modulatory neurotransmitters. The key contribution of this paper is to show how neuromodulatory effects can be modelled by adding adaptation currents to a simple phenomenological model of EEG. Critically, we show that these effects are expressed in a systematic way in the spectral density of EEG recordings. Inversion of the model, given such non-invasive recordings, should allow one to quantify pharmacologically induced changes in adaptation currents. In short, this work establishes a forward or generative model of electrophysiological recordings for psychopharmacological studies.

Broadband Cortical Desynchronization Underlies the Human Psychedelic State

Psychedelic drugs produce profound changes in consciousness, but the underlying neurobiological mechanisms for this remain unclear. Spontaneous and induced oscillatory activity was recorded in healthy human participants with magnetoencephalography after intravenous infusion of psilocybin—prodrug of the nonselective serotonin 2A receptor agonist and classic psychedelic psilocin. Psilocybin reduced spontaneous cortical oscillatory power from 1 to 50 Hz in posterior association cortices, and from 8 to 100 Hz in frontal association cortices. Large decreases in oscillatory power were seen in areas of the default-mode network. Independent component analysis was used to identify a number of resting-state networks, and activity in these was similarly decreased after psilocybin. Psilocybin had no effect on low-level visually induced and motor-induced gamma-band oscillations, suggesting that some basic elements of oscillatory brain activity are relatively preserved during the psychedelic experience. Dynamic causal modeling revealed that posterior cingulate cortex desynchronization can be explained by increased excitability of deep-layer pyramidal neurons, which are known to be rich in 5-HT2A receptors. These findings suggest that the subjective effects of psychedelics result from a desynchronization of ongoing oscillatory rhythms in the cortex, likely triggered by 5-HT2A receptor-mediated excitation of deep pyramidal cells.

Dynamic causal models of steady-state responses.

In this paper, we describe a dynamic causal model (DCM) of steady-state responses in electrophysiological data that are summarised in terms of their cross-spectral density. These spectral data-features are generated by a biologically plausible, neural-mass model of coupled electromagnetic sources; where each source comprises three sub-populations. Under linearity and stationarity assumptions, the models biophysical parameters (e.g., post-synaptic receptor density and time constants) prescribe the cross-spectral density of responses measured directly (e.g., local field potentials) or indirectly through some lead-field (e.g., electroencephalographic and magnetoencephalographic data). Inversion of the ensuing DCM provides conditional probabilities on the synaptic parameters of intrinsic and extrinsic connections in the underlying neuronal network. This means we can make inferences about synaptic physiology, as well as changes induced by pharmacological or behavioural manipulations, using the cross-spectral density of invasive or non-invasive electrophysiological recordings. In this paper, we focus on the form of the model, its inversion and validation using synthetic and real data. We conclude with an illustrative application to multi-channel local field potential data acquired during a learning experiment in mice.

Tractography-based priors for dynamic causal models

Functional integration in the brain rests on anatomical connectivity (the presence of axonal connections) and effective connectivity (the causal influences mediated by these connections). The deployment of anatomical connections provides important constraints on effective connectivity, but does not fully determine it, because synaptic connections can be expressed functionally in a dynamic and context-dependent fashion. Although it is generally assumed that anatomical connectivity data is important to guide the construction of neurobiologically realistic models of effective connectivity; the degree to which these models actually profit from anatomical constraints has not yet been formally investigated. Here, we use diffusion weighted imaging and probabilistic tractography to specify anatomically informed priors for dynamic causal models (DCMs) of fMRI data. We constructed 64 alternative DCMs, which embodied different mappings between the probability of an anatomical connection and the prior variance of the corresponding of effective connectivity, and fitted them to empirical fMRI data from 12 healthy subjects. Using Bayesian model selection, we show that the best model is one in which anatomical probability increases the prior variance of effective connectivity parameters in a nonlinear and monotonic (sigmoidal) fashion. This means that the higher the likelihood that a given connection exists anatomically, the larger one should set the prior variance of the corresponding coupling parameter; hence making it easier for the parameter to deviate from zero and represent a strong effective connection. To our knowledge, this study provides the first formal evidence that probabilistic knowledge of anatomical connectivity can improve models of functional integration.