A statistical framework for neuroimaging data analysis based on mutual information estimated via a gaussian copula

Abstract

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.

Contributions of local speech encoding and functional connectivity to audio-visual speech perception

“…This subtraction removes terms – including the statistical biases described above – that cannot possibly carry speech information (because they are computed at fixed speech envelope). This results in an estimate that is more robust and more directly related to changes in the sensory input than classical transfer entropy (the same measure was termed directed feature information in [Ince et al, 2017, Ince et al, 2015]). DI was defined here as$true0DI\left({\tau }_{Brain},{\tau }_{Speech}\right)={DI}^{\ast }\left({\tau }_{Brain}\right)-{DI}^{\ast }\left({\tau }_{Brain}\right)|Speechfalse({\tau }_{Speech}false)$…”

The Effect of Electroencephalogram (EEG) Reference Choice on Information-Theoretic Measures of the Complexity and Integration of EEG Signals

“…We computed the single-channel, joint, and conditional entropies of the EEG signals via explicit analytic expressions for the entropies based on the assumption that the EEG amplitudes realize continuous univariate and multivariate Gaussian processes with variances ${\sigma }_{\text{ii}}^2$ and covariance matrix K (Norwich, 1993; Tononi et al, 1994; van Putten and Stam, 2001; Ince et al, 2017):…”

Measuring Multivariate Redundant Information with Pointwise Common Change in Surprisal

“…We recently developed a lower-bound approximate estimator of mutual information for continuous signals based on a Gaussian copula [3]. The Gaussian I ccs measure therefore allows this approach to be used to obtain PIDs from experimental data.…”

“…However, it also provides a comprehensive statistical framework for practical data analysis [3]. For example, mutual information is closely related to the log-likelihood ratio test of independence [4].…”