Further perceptions of probability: in defence of trial-by-trial estimation models

Abstract

ABSTRACTMany events we experience are binary and probabilistic, such as the weather (rain or no rain) and the outcome of medical tests (negative or positive). Extensive research in the behavioural sciences has addressed people’s ability to learn stationary probabilities (i.e., probabilities that stay constant over time) of such events, but only recently have there been attempts to model the cognitive processes whereby people learn – and track – non-stationary probabilities. The old debate on whether learning occurs trial-by-trial or by occasional shifts between discrete hypotheses has been revived in this context. Trial-by-trial estimation models – such as the delta-rule model – have been successful in describing human learning in various contexts. It has been argued, however, that behaviour on non-stationary probability learning tasks is incompatible with trial-by-trial learning and can only be explained by models in which learning proceeds through hypothesis testing. Here, we show that this conclusion was premature. By combining two well-supported concepts from cognitive modelling – delta-rule learning and drift diffusion evidence accumulation – we reproduce all behavioural phenomena that were previously used to reject trial-by-trial learning models. Moreover, a quantitative model comparison shows that this model accounts for the data better than a model based on hypothesis testing. In the spirit of cumulative science, our results demonstrate that a combination of two well-established theories of trial-by-trial learning and evidence accumulation is sufficient to explain human learning of non-stationary probabilities.