Using alien coins to test whether simple inference is Bayesian

Monetary feedback modulates performance and electrophysiological indices of belief updating in reward learning

Belief updating entails the incorporation of new information about the environment into internal models of the world. Bayesian inference is the statistically optimal strategy for performing belief updating in the presence of uncertainty. An important open question is whether the use of cognitive strategies that implement Bayesian inference is dependent upon motivational state and, if so, how this is reflected in electrophysiological signatures of belief updating in the brain. Here, we recorded the EEG of participants performing a simple reward learning task with both monetary and nonmonetary instructive feedback conditions. Our aim was to distinguish the influence of the rewarding properties of feedback on belief updating from the information content of the feedback itself. A Bayesian updating model allowed us to quantify different aspects of belief updating across trials, including the size of belief updates and the uncertainty of beliefs. Faster learning rates were observed in the monetary feedback condition compared to the instructive feedback condition, while belief updates were generally larger, and belief uncertainty smaller, with monetary compared to instructive feedback. Larger amplitudes in the monetary feedback condition were found for three ERP components: the P3a, the feedback-related negativity, and the late positive potential. These findings suggest that motivational state influences inference strategies in reward learning, and this is reflected in the electrophysiological correlates of belief updating.

Category effects on stimulus estimation: Shifting and skewed frequency distributions-A reexamination

Duffy, Huttenlocher, Hedges, and Crawford (Psychonomic Bulletin & Review, 17(2), 224-230, 2010) report on experiments where participants estimate the lengths of lines. These studies were designed to test the category adjustment model (CAM), a Bayesian model of judgments. The authors report that their analysis provides evidence consistent with CAM: that there is a bias toward the running mean and not recent stimuli. We reexamine their data. First, we attempt to replicate their analysis, and we obtain different results. Second, we conduct a different statistical analysis. We find significant recency effects, and we identify several specifications where the running mean is not significantly related to judgment. Third, we conduct tests of auxiliary predictions of CAM. We do not find evidence that the bias toward the mean increases with exposure to the distribution. We also do not find that responses longer than the maximum of the distribution or shorter than the minimum become less likely with greater exposure to the distribution. Fourth, we produce a simulated dataset that is consistent with key features of CAM, and our methods correctly identify it as consistent with CAM. We conclude that the Duffy et al. (2010) dataset is not consistent with CAM. We also discuss how conventions in psychology do not sufficiently reduce the likelihood of these mistakes in future research. We hope that the methods that we employ will be used to evaluate other datasets.