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We begin by reviewing the statistical framework of information theory as applicable to neuroimaging data analysis. A major factor hindering wider adoption of this framework in neuroimaging is the difficulty of estimating information theoretic quantities in practice. We present a novel estimation technique that combines the statistical theory of copulas with the closed form solution for the entropy of Gaussian variables. This results in a general, computationally efficient, flexible, and robust multivariate statistical framework that provides effect sizes on a common meaningful scale, allows for unified treatment of discrete, continuous, unidimensional and multidimensional variables, and enables direct comparisons of representations from behavioral and brain responses across any recording modality. We validate the use of this estimate as a statistical test within a neuroimaging context, considering both discrete stimulus classes and continuous stimulus features. We also present examples of analyses facilitated by these developments, including application of multivariate analyses to MEG planar magnetic field gradients, and pairwise temporal interactions in evoked EEG responses. We show the benefit of considering the instantaneous temporal derivative together with the raw values of M/EEG signals as a multivariate response, how we can separately quantify modulations of amplitude and direction for vector quantities, and how we can measure the emergence of novel information over time in evoked responses. Open-source Matlab and Python code implementing the new methods accompanies this article. Hum Brain Mapp 38:1541-1573, 2017. © 2016 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Abstract: Mutual information is a principled non-linear measure of dependence between stochastic variables, which is widely used to study the selectivity of neural responses to external stimuli. Here we define and develop a set of novel statistical independence tests based on mutual information, which quantify the significance of neural selectivity to either single features or to multiple, potentially correlated stimulus features like those often present in naturalistic stimuli. If the values of different features are correlated during stimulus presentation, it is difficult to establish if one feature is genuinely encoded by the response, or if it instead appears to be encoded only as a side effect of its correlation with another genuinely represented feature. Our tests provide a way to disambiguate between these two possibilities. We use realistic simulations of neural responses tuned to one or more correlated stimulus features to investigate how limited sampling bias correction procedures affect the statistical power of such independence tests, and we characterize the regimes in which the distribution of information values under the null hypothesis can be approximated by simple distributions (Chi-square or Gaussian). Finally, we apply these tests to experimental data to determine the significance of tuning of the band limited power (BLP) of the gamma [30–100Hz] frequency range of the primary visual cortical local field potential to multiple correlated features during presentation of naturalistic movies. We show that gamma BLP carries significant, genuine information about orientation, space contrast and time contrast, despite the strong correlations between these features. [Copyright &y& Elsevier]

Abstract: Population coding is the quantitative study of which algorithms or representations are used by the brain to combine together and evaluate the messages carried by different neurons. Here, we review an information-theoretic approach to population coding. We first discuss how to compute the information carried by simultaneously recorded neural populations, and in particular how to reduce the limited sampling bias which affects the calculation of information from a limited amount of experimental data. We then discuss how to quantify the contribution of individual members of the population, or the interaction between them, to the overall information encoded by the considered group of neurons. We focus in particular on evaluating what is the contribution of interactions up to any given order to the total information. We illustrate this formalism with applications to simulated data with realistic neuronal statistics and to real simultaneous recordings of multiple spike trains. [Copyright &y& Elsevier]