Bayesian Model of Haptic Stimulus Perception
Figure 2: Bayesian model for the perception of two haptic stimuli. Before any stimulus is delivered, the subject has a prior expectation p prior ( s ) p_{\mathrm{prior}}(s) with mean μ t \mu_{t} and uncertainty width σ t \sigma_{t} . When the first stimulus of true log-intensity s t ⋆ s_{t}^{\star} is delivered at time t t , the likelihood function, of width σ ℓ \sigma_{\ell} , is maximised at an estimated stimulus s t = s t ⋆ s_{t}=s_{t}^{\star} . The prior and likelihood are combined to produce a posterior p post ( s t | s t ⋆ ) p_{\text{post}}(s_{t}|s_{t}^{\star}) according to Bayes’ ru
Paper context
Paper title: Modelling time-order effects in haptic perception with a Bayesian dynamical framework Abstract: Perceptual judgments of sequential stimuli are systematically biased by prior expectations and by the temporal structure of sensory input. In haptic discrimination tasks, these effects often manifest as time-order asymmetries, whereby the perceived difference between two stimuli depends on their presentation order. Here, we introduce a dynamical Bayesian model that accounts for these biases by combining noisy sensory measurements with an evolving internal representation of stimulus intensity. The model formalizes perception as an inference process in which prior expectations are updated by incoming stimuli and propagate in time between observations. We test the model on psychophysical data from vibrotactile discrimination experiments, in which participants compare pairs of sequential stimuli with varying intensities. With a small number of parameters, the model quantitatively reproduces both the direction and magnitude of time-order effects across subjects, as well as the observed inter-individual variability. The inferred parameters provide a compact description of perceptual biases in terms of prior expectations and noise characteristics. Beyond fitting the data, the model induces a transformation of stimulus space, leading to a subject-dependent geometry of perceived stimuli. In this transformed space, perceptual judgments exhibit approximate symmetries that are absent in the physical stimulus coordinates. These results suggest that temporal biases in perception can be und Passages referencing this figure: also provides a principled way to analyse asymmetries in perceived similarity between sequential stimuli. Consistent general features can be identified despite individual differences, and falsifiable predictions can be generated for variations of the experimental paradigm. Finally, we discuss the applicability of the model to other perceptual systems and tasks. 2 Methods 2.1 Behavioural paradigm Figure 1: A: Layout of the behavioural experiments. B: The reference and each of the comparison stimuli were presented, across different trials, in the two possible orderings. C: Probabilities q ( r , c 2 ) q(r,c_{2}) and q ( c 2 , r ) q(c_{2},r) that a given subject identify the stimuli r r and c 2 c_{2} as equal, for the two presentation orderings. Red (blue): Weakest (strongest) stimulus fi nd q ( c 2 , r ) q(c_{2},r) that a given subject identify the stimuli r r and c 2 c_{2} as equal, for the two presentation orderings. Red (blue): Weakest (strongest) stimulus first. The two probabilities are significantly different ( p = 4 ⋅ 10 − 4 p=4\cdot 10^{-4} ). To perform the vibrotactile tests, subjects positioned their index finger on a mechanical vibrating actuator rested on a sponge (Fig. 1 A), to minimize coupling with other rigid surfaces. Two consecutive stimuli were rendered with a 1-second pause between them, and participants informed via the keyboard whether they perceived them as equal or different (Fig. 1 B). For each subject and presentation order, we estimated the probability that the pair was perceived as equal. Five stimuli were used. The one with the smallest ampl ferent ( p = 4 ⋅ 10 − 4 p=4\cdot 10^{-4} ). To perform the vibrotactile tests, subjects positioned their index finger on a mechanical vibrating actuator rested on a sponge (Fig. 1 A), to minimize cou
