The Piecewise Linear Ballistic Accumulator 1 Running head: THE PIECEWISE LINEAR BALLISTIC ACCUMULATOR A new framework for modeling decisions about changing information: The Piecewise Linear Ballistic Accumulator model

In the real world, decision making processes must be able to integrate non-stationary information that changes systematically while the decision is in progress. Although theories of decision making have traditionally been applied to paradigms with stationary information, non-stationary stimuli are now of increasing theoretical interest. We developed the piecewise linear ballistic accumulator (PLBA) model to explain how decision processes are updated when a stimulus changes. The PLBA is efficient to simulate, enabling it to be fit to participant choice and response-time distribution data in a hierarchal modelling framework using a non-parametric approximate Bayesian algorithm. We applied the PLBA to a random-dot motion paradigm in which participants viewed a cloud of moving dots, where the motion switched directions midway through some trials, and were asked to determine the direction of motion. Behavioral results revealed a strong delay effect: after presentation of the initial motion direction there is a substantial time delay before the changed motion information is integrated into the decision process. Consistent with behavioral results, PLBA fits confirmed the presence of a long delay between presentation and integration of new stimulus information, but did not support increased response caution in reaction to the change. We also found the decision process was not veridical, as symmetric stimulus change had an asymmetric effect on the rate of evidence accumulation. Our results show that in this paradigm the perceptual decision process was slow to react to, and underestimated, new contrary motion information. These results support the more general utility of the PLBA model as a flexible framework for investigating decisions about changing information.