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

Extensive research in the behavioural sciences has addressed peoples ability to learn stationary probabilities, which stay constant over time, but only recently have there been attempts to model the cognitive processes whereby people learn - and track - non-stationary probabilities. In this context, the old debate on whether learning occurs by gradual formation of associations or by occasional shifts between hypotheses representing beliefs about distal states of the world has resurfaced. Gallistel et al. (2014) pitched the two theories against each other in a non-stationary probability learning task. They concluded that various qualitative patterns in their data were incompatible with trial-by-trial associative learning and could only be explained by a hypothesis-testing model. Here, we contest that claim and demonstrate that it was premature. First, we argue that their experimental paradigm consisted of two distinct tasks: probability tracking (an estimation task) and change detection (a decision-making task). Next, we present a model that uses the (associative) delta learning rule for the probability tracking task and bounded evidence accumulation for the change-detection task. We find that this combination of two highly established theories accounts well for all qualitative phenomena and outperforms the alternative model proposed by Gallistel et al. in a quantitative model comparison. In the spirit of cumulative science, we conclude that current experimental data on human learning of non-stationary probabilities can be explained as a combination of associative learning and bounded evidence accumulation and does not require a new model.