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Within neuroscience, psychology, and neuroimaging, the most frequently used statistical approach is null hypothesis significance testing (NHST) of the population mean. An alternative approach is to perform NHST within individual participants and then infer, from the proportion of participants showing an effect, the prevalence of that effect in the population. We propose a novel Bayesian method to estimate such population prevalence that offers several advantages over population mean NHST. This method provides a population-level inference that is currently missing from study designs with small participant numbers, such as in traditional psychophysics and in precision imaging. Bayesian prevalence delivers a quantitative population estimate with associated uncertainty instead of reducing an experiment to a binary inference. Bayesian prevalence is widely applicable to a broad range of studies in neuroscience, psychology, and neuroimaging. Its emphasis on detecting effects within individual participants can also help address replicability issues in these fields. Scientists use statistical tools to evaluate observations or measurements from carefully designed experiments. In psychology and neuroscience, these experiments involve studying a randomly selected group of people, looking for patterns in their behaviour or brain activity, to infer things about the population at large. The usual method for evaluating the results of these experiments is to carry out null hypothesis statistical testing (NHST) on the population mean – that is, the average effect in the population that the study participants were selected from. The test asks whether the observed results in the group studied differ from what might be expected if the average effect in the population was zero. However, in psychology and neuroscience studies, people’s brain activity and performance on cognitive tasks can differ a lot. This means important effects in individuals can be lost in the overall population average. Ince et al. propose that this shortcoming of NHST can be overcome by shifting the statistical analysis away from the population mean, and instead focusing on effects in individual participants. This led them to create a new statistical approach named Bayesian prevalence. The method looks at effects within each individual in the study and asks how likely it would be to see the same result if the experiment was repeated with a new person chosen from the wider population at random. Using this approach, it is possible to quantify how typical or uncommon an observed effect is in the population, and the uncertainty around this estimate. This differs from NHST which only provides a binary ‘yes or no’ answer to the question, ‘does this experiment provide sufficient evidence that the average effect in the population is not zero?’ Another benefit of Bayesian prevalence is that it can be applied to studies with small numbers of participants which cannot be analysed using other statistical methods. Ince et al. show that the Bayesian prevalence can be applied to a range of psychology and neuroimaging experiments, from brain imaging to electrophysiology studies. Using this alternative statistical method could help address issues of replication in these fields where NHST results are sometimes not the same when studies are repeated.

A key challenge in neuroimaging remains to understand where, when, and now particularly how human brain networks compute over sensory inputs to achieve behavior. To study such dynamic algorithms from mass neural signals, we recorded the magnetoencephalographic (MEG) activity of participants who resolved the classic XOR, OR, and AND functions as overt behavioral tasks (N = 10 participants/task, N-of-1 replications). Each function requires a different computation over the same inputs to produce the task-specific behavioral outputs. In each task, we found that source-localized MEG activity progresses through four computational stages identified within individual participants: (1) initial contralateral representation of each visual input in occipital cortex, (2) a joint linearly combined representation of both inputs in midline occipital cortex and right fusiform gyrus, followed by (3) nonlinear task-dependent input integration in temporal-parietal cortex, and finally (4) behavioral response representation in postcentral gyrus. We demonstrate the specific dynamics of each computation at the level of individual sources. The spatiotemporal patterns of the first two computations are similar across the three tasks; the last two computations are task specific. Our results therefore reveal where, when, and how dynamic network algorithms perform different computations over the same inputs to produce different behaviors.

While sensory neurons carry behaviorally relevant information in responses that often extend over hundreds of milliseconds, the key units of neural information likely consist of much shorter and temporally precise spike patterns. The mechanisms and temporal reference frames by which sensory networks partition responses into these shorter units of information remain unknown. One hypothesis holds that slow oscillations provide a network-intrinsic reference to temporally partitioned spike trains without exploiting the millisecond-precise alignment of spikes to sensory stimuli. We tested this hypothesis on neural responses recorded in visual and auditory cortices of macaque monkeys in response to natural stimuli. Comparing different schemes for response partitioning revealed that theta band oscillations provide a temporal reference that permits extracting significantly more information than can be obtained from spike counts, and sometimes almost as much information as obtained by partitioning spike trains using precisely stimulus-locked time bins. We further tested the robustness of these partitioning schemes to temporal uncertainty in the decoding process and to noise in the sensory input. This revealed that partitioning using an oscillatory reference provides greater robustness than partitioning using precisely stimulus-locked time bins. Overall, these results provide a computational proof of concept for the hypothesis that slow rhythmic network activity may serve as internal reference frame for information coding in sensory cortices and they foster the notion that slow oscillations serve as key elements for the computations underlying perception.

Understanding the operations of neural networks in the brain requires an understanding of whether interactions among neurons can be described by a pairwise interaction model, or whether a higher order interaction model is needed. In this article we consider the rate of synchronous discharge of a local population of neurons, a macroscopic index of the activation of the neural network that can be measured experimentally. We analyse a model based on physics' maximum entropy principle that evaluates whether the probability of synchronous discharge can be described by interactions up to any given order. When compared with real neural population activity obtained from the rat somatosensory cortex, the model shows that interactions of at least order three or four are necessary to explain the data. We use Shannon information to compute the impact of high-order correlations on the amount of somatosensory information transmitted by the rate of synchronous discharge, and we find that correlations of higher order progressively decrease the information available through the neural population. These results are compatible with the hypothesis that high-order interactions play a role in shaping the dynamics of neural networks, and that they should be taken into account when computing the representational capacity of neural populations.

The timing of slow auditory cortical activity aligns to the rhythmic fluctuations in speech. This entrainment is considered to be a marker of the prosodic and syllabic encoding of speech, and has been shown to correlate with intelligibility. Yet, whether and how auditory cortical entrainment is influenced by the activity in other speech–relevant areas remains unknown. Using source-localized MEG data, we quantified the dependency of auditory entrainment on the state of oscillatory activity in fronto-parietal regions. We found that delta band entrainment interacted with the oscillatory activity in three distinct networks. First, entrainment in the left anterior superior temporal gyrus (STG) was modulated by beta power in orbitofrontal areas, possibly reflecting predictive top-down modulations of auditory encoding. Second, entrainment in the left Heschl's Gyrus and anterior STG was dependent on alpha power in central areas, in line with the importance of motor structures for phonological analysis. And third, entrainment in the right posterior STG modulated theta power in parietal areas, consistent with the engagement of semantic memory. These results illustrate the topographical network interactions of auditory delta entrainment and reveal distinct cross-frequency mechanisms by which entrainment can interact with different cognitive processes underlying speech perception. [Display omitted] •We study auditory cortical speech entrainment from a network perspective.•Found three distinct networks interacting with delta-entrainment in auditory cortex.•Entrainment is modulated by frontal beta power, possibly indexing predictions.•Central alpha power interacts with entrainment, suggesting motor involvement.•Parietal theta is modulated by entrainment, suggesting working memory compensation.

Group-level statistics for extracting neurophysiological cognitive brain networks.Combining non-parametric permutations with measures of information.Fixed- and random-effect models, test- and cluster-wise corrections.Multi-level inferences, from local regions to inter-areal functional connectivity.A Python open-source toolbox called Frites includes the proposed statistical methods. The reproducibility crisis in neuroimaging and in particular in the case of underpowered studies has introduced doubts on our ability to reproduce, replicate and generalize findings. As a response, we have seen the emergence of suggested guidelines and principles for neuroscientists known as Good Scientific Practice for conducting more reliable research. Still, every study remains almost unique in its combination of analytical and statistical approaches. While it is understandable considering the diversity of designs and brain data recording, it also represents a striking point against reproducibility. Here, we propose a non-parametric permutation-based statistical framework, primarily designed for neurophysiological data, in order to perform group-level inferences on non-negative measures of information encompassing metrics from information-theory, machine-learning or measures of distances. The framework supports both fixed- and random-effect models to adapt to inter-individuals and inter-sessions variability. Using numerical simulations, we compared the accuracy in ground-truth retrieving of both group models, such as test- and cluster-wise corrections for multiple comparisons. We then reproduced and extended existing results using both spatially uniform MEG and non-uniform intracranial neurophysiological data. We showed how the framework can be used to extract stereotypical task- and behavior-related effects across the population covering scales from the local level of brain regions, inter-areal functional connectivity to measures summarizing network properties. We also present an open-source Python toolbox called Frites1 that includes the proposed statistical pipeline using information-theoretic metrics such as single-trial functional connectivity estimations for the extraction of cognitive brain networks. Taken together, we believe that this framework deserves careful attention as its robustness and flexibility could be the starting point toward the uniformization of statistical approaches. [Display omitted] .

Visual object recognition seems to occur almost instantaneously. However, not only does it require hundreds of milliseconds of processing, but our eyes also typically fixate the object for hundreds of milliseconds. Consequently, information reaching our eyes at different moments is processed in the brain together. Moreover, information received at different moments during fixation is likely to be processed differently, notably because different features might be selectively attended at different moments. Here, we introduce a novel reverse correlation paradigm that allows us to uncover with millisecond precision the processing time course of specific information received on the retina at specific moments. Using faces as stimuli, we observed that processing at several electrodes and latencies was different depending on the moment at which information was received. Some of these variations were caused by a disruption occurring 160–200 ​ms after the face onset, suggesting a role of the N170 ERP component in gating information processing; others hinted at temporal compression and integration mechanisms. Importantly, the observed differences were not explained by simple adaptation or repetition priming, they were modulated by the task, and they were correlated with differences in behavior. These results suggest that top-down routines of information sampling are applied to the continuous visual input, even within a single eye fixation. •Light reaching our eyes at different moments is processed in the brain simultaneously.•We introduce a method to uncover the processing specific to each of these moments.•Processing is different depending on when information is received on the retina.•These variations are multiple and occur within a single short fixation.•These variations are at least partly top-down in origin and translate to behavior.

The recent and rapid development of open source software tools for the analysis of neurophysiological datasets consisting of simultaneous multiple recordings of spikes, field potentials and other neural signals holds the promise for a significant advance in the standardization, transparency, quality, reproducibility and variety of techniques used to analyze neurophysiological data and for the integration of information obtained at different spatial and temporal scales. In this review we focus on recent advances in open source toolboxes for the information theoretic analysis of neural responses. We also present examples of their use to investigate the role of spike timing precision, correlations across neurons, and field potential fluctuations in the encoding of sensory information. These information toolboxes, available both in MATLAB and Python programming environments, hold the potential to enlarge the domain of application of information theory to neuroscience and to lead to new discoveries about how neurons encode and transmit information.

The cortex generates diverse neural dynamics, ranging from broadband fluctuations to narrowband oscillations at specific frequencies. Here, we investigated whether broadband and oscillatory dynamics play different roles in the encoding and transmission of visual information. We used information-theoretical measures to dissociate neural signals sharing common information (i.e., redundancy) from signals encoding complementary information (i.e., synergy). We analyzed electrocorticography (ECoG) and local field potentials (LFP) in the visual cortex of human and non-human primates (macaque) to investigate the extent to which broadband signals (BB) and narrowband gamma (NBG) oscillations conveyed synergistic or redundant information about images. In both species, the information conveyed by BB signals was highly synergistic within and between visual areas. By contrast, the information carried by NBG was primarily redundant within and between the same visual areas. Finally, the information conveyed by BB signals emerged early after stimulus onset, while NBG sustained information at later time points. These results suggest a potential dual role of BB and NBG cortical dynamics in visual processing, with broadband dynamics supporting nonlinear pattern recognition and oscillations facilitating information maintenance across the cortex.

An important question concerning inter-areal communication in the cortex is whether these interactions are synergistic, i.e. brain signals can either share common information (redundancy) or they can encode complementary information that is only available when both signals are considered together (synergy). Here, we dissociated cortical interactions sharing common information from those encoding complementary information during prediction error processing. To this end, we computed co-information, an information-theoretical measure that distinguishes redundant from synergistic information among brain signals. We analyzed auditory and frontal electrocorticography (ECoG) signals in five common awake marmosets performing two distinct auditory oddball tasks and investigated to what extent event-related potentials (ERP) and broadband (BB) dynamics encoded redundant and synergistic information during auditory prediction error processing. In both tasks, we observed multiple patterns of synergy across the entire cortical hierarchy with distinct dynamics. The information conveyed by ERPs and BB signals was highly synergistic even at lower stages of the hierarchy in the auditory cortex, as well as between auditory and frontal regions. Using a brain-constrained neural network, we simulated the spatio-temporal patterns of synergy and redundancy observed in the experimental results and further demonstrated that the emergence of synergy between auditory and frontal regions requires the presence of strong, long-distance, feedback and feedforward connections. These results indicate that the distributed representations of prediction error signals across the cortical hierarchy can be highly synergistic.Competing Interest StatementThe authors have declared no competing interest.Footnotes* 1. We have incorporated a new Method (Multivariate Co-Information: MVCo-I) for computing synergistic and redundant interactions within and between cortical regions. 2. We have improved the results' description and their interpretation in the Discussion section.* http://www.www.neurotycho.org/auditory-oddball-task