People rapidly and precisely extract summary statistics (e.g. mean and variance) of visually presented ensembles, and such statistics represent an essential part of their internal representation reflecting their environment. Recently, we reported that humans’ behavior in perceptual decision making task complies with the proposal that they handle simple visual attributes in a sampling-based probabilistic manner (Popovic et al. Cosyne 2013, VSS 2013; Fiser et al. ECVP 2013; Christensen et al. VSS 2014, ECVP 2014). In this study, we tested whether such probabilistic representations also may underlie the assessment of visual summary statistics. In each trial, subjects saw a group of circles (N=2…10, randomly chosen) of varying sizes and had to estimate either the mean or variance of sizes of the ensemble or the size of one individual circle from the group specified after the figure with the group was taken off the screen. In addition, they also reported their subjective confidence about their decisions on a trial-by-trial basis. Trials from the three tasks were tested either intermixed or by presenting them in blocks, separately. Stimuli were also presented at nine different durations (50, 75, 100, 133, 167, 200, 300, 400, or 600 msec). In accordance with previous results, participants could estimate correctly the mean, the variance and size of an element within the ensembles. Interestingly, mean estimation improved significantly as a function of the number of circles in the display (p < 0.001). More importantly, we found and increasing correlation between error and uncertainty as a function of presentation time, which is the hallmark of sampling-based probabilistic representation. Thus such probabilistic representation is not used exclusively for the simplest visual attributes, such as orientation, speed of small dots, but they also apply to representing more abstract kind of summary statistics.

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