Figure 1.
Data acquisition: EEG layout, pre-defined electrodes, sample waveform, and stimulus sequences.
The left panel shows the layout of the 128 electrodes of the EEG setup. The blue circles highlight the pre-defined fronto-central electrodes. The upper right panel shows a difference wave containing the MMN. The lower right panel illustrates the structure of the tone sequences presented in the roving oddball experiment. Tones are shown as black disks whose vertical position indicates sound frequency. The first tone presented after a train of tones of a different frequency is called a deviant (D).
Figure 2.
Hierarchical structure of the model space: models, theories, and frameworks.
The MMN models developed in this article can be organized into a tree structure. The leaves at the bottom of the tree represent individual models of trial-wise MMN amplitudes, and the nodes above represent sets of models (model families). The nodes at the third level represent modelling frameworks. Three theories (the prediction error hypothesis, the novelty detection hypothesis, and model adjustment hypothesis) were formalized under the framework of the free-energy principle (). This framework explicitly models information processing, which makes it fundamentally different from phenomenological explanations (
), such as change detection and adaptation models.
Table 1.
This table lists the response models of our 13 computational models of trial-wise MMN amplitudes.
Table 2.
Explanation of the variables in our computational models of trial-wise MMN amplitudes.
Figure 3.
Structure of free-energy based models of the MMN.
Our free-energy models of trial-wise MMN amplitudes ( in Figure 2) are cast within the general dynamic state-space framework formulated in Equation (1). In contrast to the phenomenological models, the internal states (
) represent probabilistic beliefs about the environment and evolve according to approximate Bayesian inference by free-energy minimization (
). All of these models share the Bayesian observer defined by the evolution function
and the probabilistic mental model
, but differ in their response functions
. The graph in the innermost box shows the mental model
as a probabilistic graphical model (with arrows indicating conditional dependencies). The random variables in circles are sensory inputs (
), tone categories (
), and transition probabilities (
). This mental model determines how subjects perceive, learn about and predict tone sequences. Please see Table 2 for an explanation of the mathematical notation.
Figure 4.
Posterior probabilities of the 13 MMN models.
The 13 MMN models were compared by their posterior probability given the trial-wise MMN amplitudes of all eight subjects. These posterior probabilities were computed by random effects Bayesian model selection at the group level. The bars are coloured according to the theory instantiated by each model. The model explaining trial-wise MMN amplitudes by precision weighted prediction errors on the unobservable tone category () had the highest posterior probability (
). It is closely followed by three almost equally probable “model adjustment” models (
), and the model explaining trial-wise MMN amplitudes by prediction errors on the observed log-frequency (
).
Figure 5.
Bayesian model comparison of the five MMN theories (a) and the two frameworks (b).
The bar plot in the upper panel (a) summarizes the comparison of the five model families in terms of their posterior probabilities. Each bar indicates the posterior probability of a particular MMN theory (i.e. ). The most plausible explanations of our trial-wise MMN data were provided by the model adjustment hypothesis (
) and the prediction error hypothesis (
). The lower panel (b) shows the results of comparing phenomenological (
) vs. free-energy based models (
); see Figure 2. It shows that our free-energy based models provide considerably more convincing explanations of our MMN data than traditional change detection or adaptation models (
).
Figure 6.
Figure 6a shows the average MMN amplitude as a function of the number of standards preceding the deviant. Figure 6b shows the average MMN amplitude as a function of the frequency of the deviant minus the frequency of the preceding standard (frequency change).