Zhu, Jianqiao, Sanborn, Adam N. and Chater, Nick (2017) Mental sampling in multimodal representations. Working Paper. Coventry: University of Warwick. (Unpublished)

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Abstract

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 simple sampling algorithms such as MCMC. First, the spatial structure is often best described by a Lévy flight distribution: the probability of the distance between two successive locations follows a power-law on the distances. Second, the temporal structure of the sampling that humans and other animals produce have long-range, slowly decaying serial correlations characterized as 1/f-like fluctuations. We propose that mental sampling is not done by simple MCMC, but is instead adapted to multimodal representations and is implemented by Metropolis-coupled Markov chain Monte Carlo (MC3), one of the first algorithms developed for sampling from multimodal distributions. MC3 involves running multiple Markov chains in parallel but with target distributions of different temperatures, and it swaps the states of the chains whenever a better location is found. Heated chains more readily traverse valleys in the probability landscape to propose moves to far-away peaks, while the colder chains make the local steps that explore the current peak or patch. We show that MC3 generates distances between successive samples that follow a Lévy flight distribution and 1/f-like serial correlations, providing a single mechanistic account of these two puzzling empirical phenomena.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	B Philosophy. Psychology. Religion > BF Psychology
Divisions:	Faculty of Science, Engineering and Medicine > Science > Psychology Faculty of Social Sciences > Warwick Business School
Library of Congress Subject Headings (LCSH):	Animal behavior -- Mathematical models, Human behavior -- Mathematical models, Bayesian statistical decision theory, Random walks (Mathematics), Animals -- Food
Publisher:	University of Warwick
Place of Publication:	Coventry
Official Date:	17 October 2017
Dates:	Date Event 17 October 2017 Available
Institution:	University of Warwick
Status:	Not Peer Reviewed
Publication Status:	Unpublished
Access rights to Published version:	Open Access (Creative Commons)
Open Access Version:	ArXiv

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