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Abstract:
Introduction:
In many situations, perceptual decision making (PDM) can be error prone. Standard models assume that the cause of the subjects' errors is noise, either sensory or neuronal. In this view, noise in the sensory input is considered to be uninformative to the subject. What experiments typically do not measure is the specific sensory input pattern over space and time of the stimuli. One of the standard approaches to modelling PDM, the drift-diffusion model (DDM) (1), models the input stimuli as summary statistics. Therefore with the DDM it is impossible to know whether an error may have been caused by (random) information present in the noise. We propose a Bayesian model which models the exact noisy sensory input shown to a subject in each trial. We compare this model to the standard analysis. We hypothesize that modelling the precise spatio-temporal dynamics of the stimuli will enable us to better explain PDM behaviour.
Methods:
Behavioural data (reaction time, accuracy) was collected from 24 subjects performing a perceptual decision-making task. Subjects viewed a single moving dot on a screen, randomly jumping around two target dots also present on the screen, and decided which target dot the dot was moving around. There were 4 difficulty levels, depending on the distance between the two target dots (Figure 1). We fit the behavioural data to a Bayesian model with the likelihood free Approximate Bayesian Computation (ABC, (2)) method. Two models were compared: a model equivalent to the DDM (mean input model: MM) (3), and the other incorporating the exact dot positions (visual stimuli) as input (exact input model: EM). The mechanism in which the input dots were created (drawn from a Gaussian distribution with mean as the target dot position, and fixed noise standard deviation over difficulty levels) was deployed as the generative model in the decision model. To compare models, we used Bayesian model selection (BMS) (4). We also calculated the posterior predictive likelihoods (PPL) to quantify how good a model can capture a subject's response on the single-trial level.
Results:
The model comparison result is shown in Figure 2A. The exceedance probability of EM is 1.00 compared to MM's 0.00 which means that the belief that the EM is more likely than the MM is 100. The posterior model probability of the EM is on average above 90 (Figure 2A, brackets), which is above chance level (50). This means that the probability that the EM generated any randomly selected subject data is above 90. Especially, the EM explained significantly more error trials compared to the MM (Figure 2B). Figure 3 shows exemplarily how the posterior probabilities of the models are evolving dynamically along with the actual dot positions. In summary our results show that by incorporating the exact input stimuli shown to subjects, the predicted response distribution gives a more accurate account of subject behaviour.
Conclusions:
Our proposed model can account better for errors caused by (random) noise evidence in support of an incorrect decision alternative, in comparison to the standard model (DDM). We suggest that modelling random spatiotemporal dynamics as typically used in perceptual decision making experiments provides for better predictions of behavioural responses at the single trial level. If this approach is used, we expect an overall increase of predictive power of perceptual decision making models and a better resolution about the underlying mechanism of perceptual decision making, at the single trial level.
