Previous research has shown that people are able to use distributional information about the environment to make inferences. However, how people learn these probability distributions is less well understood, especially for those that are not normal or unimodal. In this paper we focus on how people learn probability distributions that are bimodal. We examined on how the distance between the two peaks of a bimodal distribution and the numbers of observations influence how participants learn each distribution, using two types of stimuli with different degrees of perceptual noise. Overall, participants were able to learn the various distributions quickly and accurately. However, their performance is moderated by stimuli type—whether participants were learning a distribution over numbers (low noise) or over sizes of circles (high noise). This work suggests that although people are able to quickly learn a variety of distributions, many factors may influence their performance.

In this paper we explore a cognitive modeling approach to aggregating individuals’ estimates of unknown quantities without natural bounds. We carried out two experiments that elicited individuals’ estimates of the population of US metropolitan areas, and domestic box office returns for movies. We found that the means of individuals’ responses correlate well with the true sizes, but participants systematically underestimated these values. We formulated a cognitive model that uses the true values of known items to correct for individuals’ biases, and demonstrated that this model can drastically improve predictive accuracy. Because our model quantitatively infers individual’s biases on the estimation tasks we were able to examine the distribution of individual biases, and found that there were substantial between-individual differences in the magnitude of the responses. This work demonstrates how individuals’ biases, whether over- or underestimation, can be corrected using a cognitive model together with known ground truths