Uncovering mental representations with Markov chain Monte Carlo

A key challenge for cognitive psychology is the investigation of mental representations, such as object categories, subjective probabilities, choice utilities, and memory traces. In many cases, these representations can be expressed as a non-negative function defined over a set of objects. We present a behavioral method for estimating these functions. Our approach uses people as components of a Markov chain Monte Carlo (MCMC) algorithm, a sophisticated sampling method originally developed in statistical physics. Experiments 1 and 2 verified the MCMC method by training participants on various category structures and then recovering those structures. Experiment 3 demonstrated that the MCMC method can be used estimate the structures of the real-world animal shape categories of giraffes, horses, dogs, and cats. Experiment 4 combined the MCMC method with multidimensional scaling to demonstrate how different accounts of the structure of categories, such as prototype and exemplar models, can be tested, producing samples from the categories of apples, oranges, and grapes.