At the Zebra Crossing: Modelling Complex Decision Processes with Variable-Drift Diffusion Models

Abstract

Drift diffusion (or evidence accumulation) models have found widespread use in the modelling of simple decision tasks. Extensions of these models, in which the model’s instantaneous drift rate is not fixed but instead allowed to vary over time as a function of a stream of perceptual inputs, have allowed these models to account for more complex sensorimotor decision tasks. However, many real-world tasks seemingly rely on a myriad of even more complex underlying processes. One interesting example is the task of deciding whether to cross a road with an approaching vehicle. This action decision seemingly depends on sensory information both about own affordances (whether one can make it across before the vehicle) and action intention of others (whether the vehicle is yielding to oneself). Here, we compared three extensions of a standard drift diffusion model, with regards to their ability to capture timing of pedestrian crossing decisions in a virtual reality environment. We find that a single variable-drift diffusion model (S-VDDM) in which the varying drift rate is determined by visual quantities describing vehicle approach and deceleration, saturated at an upper and lower bound, can explain multimodal distributions of crossing times well across a broad range vehicle approach scenarios. More complex models, which attempt to partition the final crossing decision into constituent perceptual decisions, improve the fit to the human data but further work is needed before firm conclusions can be drawn from this finding.

Learning to interpret novel eHMI: The effect of vehicle kinematics and eHMI familiarity on pedestrians' crossing behaviour

“…Figure 5a illustrates that 40% of participants crossed the road in the non-decelerating trials, when the vehicle was over 42.5 m away, and, therefore, before it started to decelerate. This finding is similar to the results reported in Lee et al (2019b), which showed that 51 % of pedestrians crossed the road before the vehicle started to decelerate (see also Giles et al, 2019, Markkula et al, 2018Schneemann & Gohl., 2016). For the decelerating trials, 100% of pedestrians crossed the road, although different patterns were observed for the different eHMI conditions.…”

“…Most of the crossings were made either when the approaching vehicle was more than 42.5 m away, or when the vehicle had come to a near-(between 2.5 -5 m away) or complete-(2.5 m away) stop. These bimodal crossing patterns have been observed in previous simulation models and test-track studies (Giles et al, 2019;, Markkula et al, 2018Schneemann & Gohl., 2016), and support suggestions that the vehicle does not need to come to a full stop for a crossing pedestrian (Lee et al, 2020). This bimodal crossing pattern also suggests that pedestrians were more comfortable crossing the road either when the vehicle was quite far away, or waited until the yielding behaviour of the vehicle was more prominent, i.e.…”

“…More crossings were observed immediately after the FH was perceivable, leading to a less obvious bimodal crossing pattern, which is often seen in pedestrian crossing studies (Giles et al, 2019;, Markkula et al, 2018Schneemann & Gohl., 2016). The CIT-Change values were also found to be significantly larger for FH than SPLB, demonstrating that it was a more effective external communication design than SPLB.…”

Variable-drift diffusion models of pedestrian road-crossing decisions

“…We and others have investigated the application of drift diffusion-type models in the road traffic context, with promising results initially for low-level locomotion decisions on applying braking or steering control [39,48,71], more recently also extending to multi-agent interaction situations [2,24,31,41,73].…”

Accumulation of continuously time-varying sensory evidence constrains neural and behavioral responses in human collision threat detection

“…Third, we show that established evidence accumulation models of decision-making can be extended beyond typical laboratory paradigms with static or intermittently changing abstract stimuli, to a task with clear real-world relevance, and continuously time-varying sensory evidence. We and others have reported that evidence accumulation models show promise for modelling decisions in real-world tasks, e.g., when to apply brakes in response to a developing collision threat [52], [53], [61], or on whether and when to cross a road with oncoming traffic [62], [63]. However, in these types of naturalistic tasks it has not been possible to fit full response time probability distributions per participant, a minimum expectation in evidence accumulation modelling of more typical, abstract laboratory tasks.…”