Table 1.
Experimental Manipulations.
Fig 1.
Lissajous figure and distribution of perceptual phase durations.
(A) Lissajous are generated by the intersection of two sinusoids with perpendicular axes and increasing phase-shift whose frequency determines the speed of illusory 3D rotation. Following their introduction to experimental psychology, Lissajous figures were originally studied by means of twin-oscillators and analog cathode ray oscillographs in the 1940s and 1950s [6]. (B) Perceptual phase duration across all participants, runs and conditions. Distributions with a sharp rise and a long tail are typical of bistable perception.
Fig 2.
(A) The prior distribution ‘perceptual stability’ is defined by its mean μstability (corresponding to the perceptual decision made at the last self-occluding configuration, see ‘Percept update’-arrow) and its precision πstability. If a new percept was reported at the preceding trial, πstability is set to πinit produce a weighted bimodal distribution P(θ), which is in a next step transformed by a unit-sigmoid function determined by parameter ζ and used to predict the perceptual outcome θ. The difference between P(θ = 1) and θ constitutes the prediction error (PE). (B) In this illustration with exemplary Gaussian probability distributions, the prior distribution ‘perceptual stability’ is defined by its mean μstability (blue line) and its precision πstability (the inverse of its variance depicted in green). This prior distribution is combined with a bimodal likelihood distribution. The weighted bimodal distribution is used to predict the percept indicated by the subject at that trial (defined by its mean θ depicted in cyan and the inverse of its variance shown in purple). The difference between the weighted bimodal distribution and the percept is highlighted in red and constitutes a prediction error signal, which is used to adjust the prior distribution ‘perceptual stability’.
Fig 3.
Distribution of button presses indicating perceptual transitions.
Separately for all four conditions, transitions are plotted relative to the phase shift (i.e., degree of illusory rotation, 0–360°) of the Lissajous figure. The four panels show absolute frequencies of reported transitions across all participants. For the “slow” conditions (upper panels), the inner dashed circles of the polar plots denote 100, the outer circles denote 200. For the “fast” conditions (lower panels), the inner dashed circles of the polar plots denote 50, the outer circles denote 100. Self-occlusions of the Lissajous figure occurred at 0 and 180° (indicated by red color). Note that 10° of illusory rotation correspond to 0.2s in the “slow” and 0.1s in the “fast” conditions, leading to an increased offset between the self-occlusion positions and the distribution of transitions relative to degree of illusory rotation. Response times (RT) in all four conditions were calculated as the difference between the time points of button presses and the onsets of the preceding overlaps and are expressed as mean ± standard error of the mean.
Fig 4.
Results of the standard and Bayesian data analysis.
(A) Average transition probabilities separately for the four conditions, averaged across runs and participants. Error bars indicate the standard error of the mean. (B) Posterior parameter estimates for πinit. Posterior parameters averaged across runs and participants, separately for all conditions.