  Trial history biases in decision-making tasks are thought to reflect
systematic updates of decision variables, therefore their precise nature
informs conclusions about underlying heuristic strategies and learning
processes. However, random drifts in decision variables can corrupt this
inference by mimicking the signatures of systematic updates. Hence, identifying
the trial-by-trial evolution of decision variables requires methods that can
robustly account for such drifts. Recent studies (Lak'20, Mendon\c{c}a'20) have
made important advances in this direction, by proposing a convenient method to
correct for the influence of slow drifts in decision criterion, a key decision
variable. Here we apply this correction to a variety of updating scenarios, and
evaluate its performance. We show that the correction fails for a wide range of
commonly assumed systematic updating strategies, distorting one's inference
away from the veridical strategies towards a narrow subset. To address these
limitations, we propose a model-based approach for disambiguating systematic
updates from random drifts, and demonstrate its success on real and synthetic
datasets. We show that this approach accurately recovers the latent trajectory
of drifts in decision criterion as well as the generative systematic updates
from simulated data. Our results offer recommendations for methods to account
for the interactions between history biases and slow drifts, and highlight the
advantages of incorporating assumptions about the generative process directly
into models of decision-making.
