Big Data, Granger Causality Analysis, and the Undecidability Property of Neuroimaging

Abstract

Much excitement has surrounded the idea of ‘big data’ and its potential to drive science into a new epistemological era–one of data-intensive exploration. However, there are open interpretive questions regarding how to interpret results derived from such massive and (nearly)-complete data sets. One view of big data, called here the ‘End of Theory’ (EOT) view, advocates that identifying statistical patterns in large data sets is sufficient for generating scientific results. The present paper demonstrates that EOT is untenable in at least one big data environment in neuroscience: Granger causality analysis (GC). The present paper systematically outlines the foundations for GC and its neural correlate Granger-Geweke causality analysis (GGC) by drawing on statistics and information theory. In doing so, the present paper introduces new terminology that clarifies the role of GGC in the era of big data and establishes a standard for result interpretation. Specifically, the “undecidability property of neuroimaging” (UPN) is introduced. The need for UPN is demonstrated by the concept resolving an existing conflict in the literature that occurred in the late 2010s between Barrett _et al._ (2018a [https://doi.org/10.1073/pnas.1714497115]; 2018b [https://doi.org/10.1016/j.neuroimage.2018.05.067]) and Stokes and Purdon (2017a [https://arxiv.org/abs/1709.10248]; 2017b [https://doi.org/10.1073/pnas.1704663114]). UPN is then applied to a current research thread in cognitive neuroscience to develop a standard for how to interpret positive and null results from GGC during big data ‘exploratory analyses.’