Human representation of multimodal distributions as clusters of samples

Behavioral and neuroimaging evidence shows that human decisions are sensitive to the statistical regularities (mean, variance, skewness, etc.) of reward distributions. However, it is unclear what representations human observers form to approximate reward distributions, or probability distributions in general. When the possible values of a probability distribution are numerous, it is cognitively costly and perhaps unrealistic to maintain in mind the probability of each possible value. Here we propose a Clusters of Samples (CoS) representation model: The samples of the to-be-represented distribution are classified into a small number of clusters and only the centroids and relative weights of the clusters are retained for future use. We tested the behavioral relevance of CoS in four experiments. On each trial, human subjects reported the mean and mode of a sequentially presented multimodal distribution of spatial positions or orientations. By varying the global and local features of the distributions, we observed systematic errors in the reported mean and mode. We found that our CoS representation of probability distributions outperformed alternative models in accounting for subjects' response patterns. The ostensible influence of positive/negative skewness on the over/under estimation of the reported mean, analogous to the "skewness preference" phenomenon in decisions, could be well explained by models based on CoS.