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Mehrdad Jazayeri, Michael N. Shadlen; Probabilistic nature of time perception. Journal of Vision 2009;9(8):1090. doi: 10.1167/9.8.1090.
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We use our internal sense of time to identify temporal relationships between events and to make time-sensitive responses. The accuracy with which we can exploit temporal contingencies derives from two important factors: the temporal regularities between external stimuli and the reliability of our internal sense of time.
We used a “Ready, Set, Go” paradigm to examine how these two forms of uncertainty influence timing behavior. Human subjects were presented with two brief peripheral flashes, a “Ready” cue followed by a “Set” cue. These cues demarcated a reference interval (RI) that varied randomly from trial to trial. Subjects were instructed to reproduce RI by making a key press RI time units after “Set”. Subjects' timing accuracy were tested in three separate blocks of trials in which RIs were sampled from three partially overlapping Uniform distributions, which varied between 493–847, 670–1024, and 847–1200 ms, respectively. These distributions constitute different prior probability distributions of RI.
Behavioral responses exhibited three characteristic features. (1) Production times increased with RI. (2) Production times were systematically biased towards the mean of the prior distribution over RI. Thus, in different blocks with different prior distributions, production times associated with the same RI were biased differently. (3) The magnitude of the bias increased for longer RIs - both within and across blocks.
These observations were naturally explained in a Bayesian framework in which subjective estimates of RIs were assumed to derive from the probabilistic fusion of the likelihood information associated with a sample RI, and the prior distribution over RI. Our analysis suggests that (i) subjects were able to evaluate the uncertainty associated with the likelihood information on a trial-by-trial basis, and (ii) subjects' estimate of the prior information (i.e. “subjective prior”) depended on both the experimentally imposed prior and the subjects' timing uncertainty.
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