PT - JOURNAL ARTICLE AU - Mattias Forsgren AU - Peter Juslin AU - Ronald van den Berg TI - Further perceptions of probability: in defence of trial-by-trial updating models AID - 10.1101/2020.01.30.927558 DP - 2020 Jan 01 TA - bioRxiv PG - 2020.01.30.927558 4099 - http://biorxiv.org/content/early/2020/01/31/2020.01.30.927558.short 4100 - http://biorxiv.org/content/early/2020/01/31/2020.01.30.927558.full AB - Extensive research in the behavioural sciences has addressed people’s ability to learn probabilities of stochastic events, typically assuming them to be stationary (i.e., constant over time). Only recently have there been attempts to model the cognitive processes whereby people learn – and track – non-stationary probabilities, reviving the old debate on whether learning occurs trial-by-trial or by occasional shifts between discrete hypotheses. Trial-by-trial updating models – such as the delta-rule model – have been popular in describing human learning in various contexts, but it has been argued that they are inadequate for explaining how humans update beliefs about non-stationary probabilities. Specifically, it has been claimed that these models cannot account for the discrete, stepwise updating that has been observed in data. Here, we demonstrate that the rejection of trial-by-trial models was premature for two reasons. First, our experimental data suggest that the stepwise behaviour depends on details of the experimental paradigm. Hence, discreteness in response data does not necessarily imply discreteness in internal belief updating. Second, previous studies have dismissed trial-by-trial models mainly based on qualitative arguments rather than quantitative model comparison. To evaluate the models more rigorously, we performed a likelihood-based model comparison between stepwise and trial-by-trial updating models. Across eight datasets collected in three different labs, human behaviour is consistently best described by trial-by-trial updating models. Our results suggest that trial-by-trial updating plays a prominent role in the cognitive processes underlying learning of non-stationary probabilities.