Drift-diffusion models (DDM) have had empirical success in fitting choice and reaction time behavior as well as electrophysiological recordings during binary choice. The standard assumption is that evidence accumulates according to an (unobserved) underlying stochastic process with a drift that depends on the stimulus, but usually neither on the state of the accumulator nor on time. Here, we present a behavioral experiment designed to directly visualize the “drifting particle” of the DDM by measuring how choice accuracy evolves with time. This permits more direct inference on the form of the underlying stochastic process than do traditional approaches, allowing us to better differentiate between competing models of evidence accumulation.

METHODS

In each of 360 trials, our 159 subjects were briefly shown (simultaneously) 100 small circles (some red, some blue), and were asked whether the majority of these were red or blue. After their response, we elicited subjects’ probabilistic beliefs (or confidence) that their preceding choice was correct. We systematically varied the duration for which the circles were visible prior to onset of a visual mask. Three treatments are examined: unpredictable-time-of-offset, unpredictable-time-of-onset, and free-response (which corresponds to a standard reaction time experiment). Finally, separate blocks of trials also manipulated the prior probability of “red” being the correct response. 

RESULTS

As expected and previously demonstrated, choice accuracy increases as a function of the time during which the dots are displayed. Increasing signal strength scales these curves, while changes in prior probability shift them in their early stages. The influence of the prior on the decision variable decays over time. The rate at which evidence accumulates over time is revealed as a function of signal strength and prior, allowing us to quantitatively compare this process with the predictions of the DDM. One striking feature we observed was that evidence against the prior accumulates at a faster rate than evidence in favor of the prior. Reported confidence is linearly correlated with the accuracy of the decisions, and provides further empirical restrictions on the model.

CONCLUSIONS

Visualizing the “drifting particle” using this experimental methodology allows us to infer the form of the stochastic process according to which evidence accumulates. While the DDM approximates key features of this process quite well, preliminary analysis of our data suggests that it can be improved upon by considering more general stochastic processes, for example one with a drift rate that depends on the state of the accumulator.