Both resources in the natural environment and concepts in a semantic space are distributed patchily, with large gaps in between the patches. To describe people's internal and external foraging behavior, various random walk models have been proposed. In particular, internal foraging has been modeled as sampling: in order to gather relevant information for making a decision, people draw samples from a mental representation using random-walk algorithms such as Markov chain Monte Carlo (MCMC). However, two common empirical observations argue against people using simple sampling algorithms such as MCMC for internal foraging. First, the distance between samples is often best described by a Levy flight distribution: the probability of the distance between two successive locations follows a power-law on the distances.

One of the current speculative hypotheses in cognition is that the brain performs approximate Bayesian inference via some form of sampling algorithm. Based on this assumption, this paper explores which kind of Monte Carlo algorithm the brain might be using. In particular, previous work has proposed direct sampling (DS) from the posterior distribution, or random-walk MCMC. However, these two algorithms are unable to explain some empirically observed features of mental representations, such as the power law seen in the distance between consecutive, distinct "samples" (such as responses in a semantic fluency task) or, equivalently under certain assumptions, of the distribution of inter-response intervals. This paper argues that another type of MCMC algorithm, that is MC3 aka parallel tempering, which is a MCMC method designed to deal with multimodal, patchy posteriors (hence the "foraging" analogy), is instead able to explain these features.

Both resources in the natural environment and concepts in a semantic space are distributed "patchily", with large gaps in between the patches. To describe people's internal and external foraging behavior, various random walk models have been proposed. In particular, internal foraging has been modeled as sampling: in order to gather relevant information for making a decision, people draw samples from a mental representation using random-walk algorithms such as Markov chain Monte Carlo (MCMC). However, two common empirical observations argue against people using simple sampling algorithms such as MCMC for internal foraging. First, the distance between samples is often best described by a Levy flight distribution: the probability of the distance between two successive locations follows a power-law on the distances.