Abstract
Predictive coding postulates that we make (top-down) predictions about the world and that we continuously compare incoming (bottom-up) sensory information with these predictions, in order to update our models and perception so as to better reflect reality. That is, our so-called “Bayesian brains” continuously create and update generative models of the world, inferring (hidden) causes from (sensory) consequences. Neuroimaging datasets enable the detailed investigation of such modeling and updating processes, and these datasets can themselves be analyzed with Bayesian approaches. These offer methodological advantages over classical statistics. Specifically, any number of models can be compared, the models need not be nested, and the “null model” can be accepted (rather than only failing to be rejected as in frequentist inference). This methodological paper explains how to construct posterior probability maps (PPMs) for Bayesian Model Selection (BMS) at the group level using electroencephalography (EEG) or magnetoencephalography (MEG) data. The method has only recently been used for EEG data, after originally being developed and applied in the context of functional magnetic resonance imaging (fMRI) analysis. Here, we describe how this method can be adapted for EEG using the Statistical Parametric Mapping (SPM) software package for MATLAB. The method enables the comparison of an arbitrary number of hypotheses (or explanations for observed responses), at each and every voxel in the brain (source level) and/or in the scalp-time volume (scalp level), both within participants and at the group level. The method is illustrated here using mismatch negativity (MMN) data from a group of participants performing an audio-spatial oddball attention task. All data and code are provided in keeping with the Open Science movement. In doing so, we hope to enable others in the field of M/EEG to implement our methods so as to address their own questions of interest.
Highlights
The statistical testing of hypotheses originated with Thomas Bayes (Neyman and Pearson, 1933), whose famous eponymous theorem (Bayes and Price, 1763) can be written in terms of probability densities as follows:p θ|y p y θ)p(θ) = p(y) (1)Bayesian Model Selection (BMS) Maps Using magnetoencephalography (MEG) data (M/EEG) Data where θ denotes unobserved parameters, y denotes observed quantities, and p(θ|y) denotes the probability p of the unknown parameters θ, given (“|”) the set of observed quantities y
Model did have over 75% model probability centrally between 175–185 ms, which is within the mismatch negativity (MMN) time window
This paper shows how to use RFX BMS mapping methods for M/EEG data analysis
Summary
Bayes conceptualizes statistics as the plausibility of a hypothesis given the knowledge available (Meinert, 2012). Bayes’ theorem allows one to update one’s knowledge of the previously estimated (or “prior”) probability of causes, to a new estimate, the “posterior” probability of possible causes. This process can be repeated indefinitely, with the prior being recursively updated to the new posterior each time. This gives rise to multiple intuitive and useful data analysis methods, one of which is the explained in detail in this paper
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