Fig 1.
A. In the modelling approach illustrated here, we capture the temporal dynamics of bistable perception by changes in a continuously updated stability prior, which is combined with a bimodal likelihood representing the sensory input (see ‘feedback’ arrow). Under ambiguous viewing conditions, the likelihood contains equivalent evidence for both perceptual interpretations of the bistable stimulus. The mean of the prior ‘perceptual stability’ is defined by μstability, which corresponds to the preceding perceptual decision y(t − 1) (here centered around ‘1’ for counter-clockwise rotation of the Lissajous figure). The impact of the prior on the bimodal likelihood is determined by its precision (the inverse of variance) πstability. If a new perceptual decision was adopted at the preceding overlapping configuration of the Lissajous figure, this precision is set to πinit. Otherwise, πstability is repeatedly updated by a prediction error signal. This signal results from residual evidence for the alternative explanation of the bistable stimulus and is given by the difference between P(θ > 0.5) and the current perceptual decision y(t) (see ‘feedforward’ arrow). In this example, the prediction error signal stems from remaining evidence for clockwise rotation (centered around ‘0’), as the current perceptual decision represents counter-clockwise rotation (y(t) = 1) of the stimulus. Overtime, the stability prior is weakened, which is accompanied by an increasing probability for a novel transition in perception. B. Here, we depict the temporal evolution of the stability prior (left panel) and the corresponding posterior (right panel) at three successive overlapping configurations of the Lissajous figure (dark to light blue). As the precision of the stabilizing prior is gradually reduced, the posterior relaxes to equivalent probability for both perceptual interpretations of the stimulus. This is accompanied by escalating prediction error signals and increased likelihood for a perceptual transition. C. Furthermore, our approach accounts for additional sensory evidence, which is realized by a stereodisparity signal and used to disambiguate the Lissajous figure in the ‘replay’ condition. To this end, we introduce a ‘stereodisparity’ distribution (characterized by mean μstereo and precision πstereo), which serves as a weight on the bimodal likelihood. In the ambiguous condition (left panel), μstereo is centered around 0.5 and is thus uninformative with regard to the two perceptual interpretations of the stimulus. In the replay condition (right panel), μstereo is centered around ‘0’ or ‘1’ (depending on the direction of stereodisparity). The strength of the bias in the direction of either percept introduced by the stereodisparity signal scales with the precision πstereo.
Table 1.
Summary of model parameters and quantities.
Fig 2.
Simulating perceptual decisions during ambiguous stimulation.
Data were simulated using πinit of 3.5 at a sampling rate of 0.33 Hz for a total of 6*105 seconds. The distribution of phase durations followed a sharp rise and slow fall resembling a gamma-distribution. The insets A-C show simulated perceptual time-courses (grey dotted lines) next to updated model quantities (black solid lines). A: Prediction errors increase during a dominance phase and are reduced by perceptual transitions. B: Bistable perception can be conceived as resulting from subsequent sampling from a bimodal probability distribution [19], the weight of which is expressed by P(θ > 0.5). This weight is close to 0 or 1 at the beginning of a dominance phase (low transition probability) and gradually relaxes to 0.5 (high transition probability). C: The variance (inverse precision) of the prior distribution ‘perceptual stability’ increases as a consequence of prediction errors and is set to 1/πinit after a transition in perception.
Fig 3.
A: The geometric mean (i.e. the arithmetic mean in log-space) of posterior πinit and πstereo, averaged across runs and participants, and standard error of the mean. B: Mean prediction errors averaged across runs and participants for ambiguous and replay blocks and standard error of the mean. Prediction errors were significantly decreased during replay stimulation (two-sample t-test, p < 10−6, t19 = 7.69). C: Average transition probabilities correlated significantly with average πinit for individual participants (ρ = −0.88, p < 10−7, Pearson correlation), providing a sanity check for model fit. D: Transition probabilities from run 3 were predictive of posterior πinit averaged over run 1 and 2. The significant Pearson correlation between the two independent measures (ρ = −0.76, p < 10−4) illustrates the predictive power of the model.
Table 2.
‘PE model’: Overlaps vs baseline.
Table 3.
‘Conventional model’: Overlaps vs baseline.
Table 4.
‘Block model’: Overlaps vs baseline.
Fig 4.
Model-based fMRI results from standard GLM (A, B) and PPM (C) analyses.
GLMs are displayed using FWE correction at p < 0.05. For PPM results, we show voxels above an exceedance probability of 99% with a cluster size n > 10. A: 2-level contrast for ‘Transition vs. baseline’ showing activations left pre- and postcentral gyrus, right inferior frontal gyrus, right inferior parietal lobulus and right middle frontal gyrus with qualitatively equivalent results for all models. B: ‘PE vs. baseline’ (‘PE model’) yielded activations in bilateral insulae and inferior frontal gyri. We found no whole-brain correctable voxels for ‘Ambiguity vs. baseline’ (‘Block model’) nor for ‘Ambiguous vs. replay transitions’ (‘Conventional model’). C: Group exceedance probability maps with right insula, right inferior frontal gyrus, right posterior-medial frontal gyrus as well as left precentral gyrus showed strongest evidence for the ‘PE model’ as compared to the control models.
Table 5.
‘PE model’: Transitions vs baseline.
Table 6.
‘Conventional model’: Transitions vs baseline.
Table 7.
‘Block model’: Transitions vs baseline.
Fig 5.
Average eigenvariate time-courses.
For visualization, we extracted eigenvariate time-courses from right insula, left insula, right IFG and left IFG (A–D), aligned all phase durations to the timepoint of the upcoming perceptual transition and averaged within and across observers. In analogy to modelled prediction error trajectories, mean eigenvariate time-courses (± standard error of the mean) showed a gradual increase towards a transition in perception.