Exploring Sampling Algorithms to explain Cognitive Characteristics in Random Number Sequences and a Time-estimation Task

Abstract

Recently, sampling algorithms have demonstrated their ability in simulating ubiquitous cognitive characteristics, such as autocorrelations and levy-like distributions, found in foraging behaviours. However, this effect has been observed independently in individual tasks. Exploring the co-occurrence of such phenomena has yet to be investigated. This paper explores three main questions: Whether two foraging characteristics co-occur, whether cognitive load impacts said foraging characteristics and to what extent can sampling algorithms explain these cognitive characteristics. Seven participants were given two sequential tasks (Random number generation (RNGT) and a metronome tapping task) separately as well as together. The findings suggest that foraging does not co-occur; that autocorrelations are present in the tapping task but not RNGT and heavy tailed distributions are present in RNGT but not in the tapping task. Cognitive load only plays a role in the tapping task. Further analysis explored task-specific cognitive characteristics outlining potential strategies and patterns participants used (including randomness, run length, pattern type and jump length) and the findings were compared to four sampling algorithms: A Direct Sampler (DS), Markov Chain Monte Carlo (MCMC), Metropolis-Coupled Markov Chain Monte Carlo (MC3) and a No-U turn Hamiltonian Monte Carlo (HMC). The DS, MC3 and HMC were able to produce similar results to human behaviour but identifies that a hybrid approach of these three samplers might simulate the metrics produced by humans better.