Journal: PLOS Biology

Article Title: Rewarding animals based on their subjective percepts is enabled by online Bayesian estimation of perceptual biases

doi: 10.1371/journal.pbio.3002764

Figure Lengend Snippet: ( A ) The mean (solid curves) and the standard deviation (SD, shaded areas) of the inferred perceptual (red in the rightward and green in the leftward self-motion conditions) and decision (blue, neutral, no self-motion condition) biases for an example synthetic data set. Ground truth perceptual bias was +20 in the leftward self-motion condition (dashed red) and –10 in the rightward self-motion condition (dashed green). The decision bias common to all conditions was +10, as seen in the neutral, no self-motion condition (dashed blue). Before one data point was collected for each unique stimulus (first 33 trials), posterior distributions over the biases were not yet available. Therefore, we show prior distributions in this interval, with the mean (solid lines) and standard deviation (shaded areas) depicted. ( B ) The same as (A), but showing an example synthetic dataset with a slowly changing decision bias. ( C ) Average root mean square error (RMSE, y-axis), across 100 simulations, in estimating perceptual bias in the rightward self-motion condition, plotted as a function of trial number. Results are shown for three different prior mean values: 0, 1, and 2 SDs away from the ground truth perceptual bias (from light to dark green, respectively). The black curve demonstrates results for a maximum likelihood estimator which corresponds to a Bayesian estimator with a uniform prior. ( D ) Average root mean square error (RMSE, y-axis), over 100 simulations, in estimating perceptual bias in the rightward self-motion condition for three different values of prior widths for perceptual and decision biases (solid curves, light green to dark green, respectively). See text for details. Dashed curves show analogous results obtained using the conventional Bayesian Psignifit library. ( E ) The same simulation as in (C), but the SD of the perceptual bias averaged over 100 simulations is plotted. ( F ) The same simulation in (D), but the SD of the perceptual bias over 100 simulations is plotted. Source data for – are available in “simulation_data/Figure5A.mat”—“simulation_data/Figure5DF_stan.mat” at https://doi.org/10.5281/zenodo.15341390 .

Article Snippet: We used Gibbs sampling using the STAN Matlab toolbox [ – ] to compute the posteriors over the perceptual and decision biases ( P L , P R , and D ), the sensory noise variables ( S L , S N , and S R ), and the lapse rates ( λ 1 , k and λ 2 , k ).

Techniques: Standard Deviation