Foraging as sampling without replacement: A Bayesian statistical model for estimating biases in target selection

Abstract

Foraging entails finding multiple targets sequentially. In humans and other animals, a key observation has been a tendency to forage in ‘runs’ of the same target type. This tendency is context-sensitive, and in humans, it is strongest when the targets are difficult to distinguish from the distractors. Many important questions have yet to be addressed about this and other tendencies in human foraging, and a key limitation is a lack of precise measures of foraging behaviour. The standard measures tend to be run statistics, such as the maximum run length and the number of runs. But these measures are not only interdependent, they are also constrained by the number and distribution of targets, making it difficult to make inferences about the effects of these aspects of the environment on foraging. Moreover, run statistics are underspecified about the underlying cognitive processes determining foraging behaviour. We present an alternative approach: modelling foraging as a procedure of generative sampling without replacement, implemented in a Bayesian multilevel model. This allows us to break behaviour down into a number of biases that influence target selection, such as the proximity of targets and a bias for selecting targets in runs, in a way that is not dependent on the number of targets present. Our method thereby facilitates direct comparison of specific foraging tendencies between search environments that differ in theoretically important dimensions. We demonstrate the use of our model with simulation examples and re-analysis of existing data. We believe our model will provide deeper insights into visual foraging and provide a foundation for further modelling work in this area.

Visual search habits and the spatial structure of scenes

“…The role of spatial layout in driving the individual differences observed in foraging (Kristjánsson et al, 2014 ) noted in the introduction is an interesting question for future research to explore. Recent efforts to measure both spatial and target selection biases in foraging (Clarke, Hunt, & Hughes, 2022a ) offers the potential for new insights into how and when observers use spatial layout to guide sequential target selections.…”

A Bayesian Statistical Model Is Able to Predict Target-by-Target Selection Behaviour in a Human Foraging Task

“…We will make use of the foraging model from Clarke et al (2022) [ 7 ]. This treats foraging as a sampling without replacement process in which each item i has probability of being selected as the next target.…”

“…This model is implemented in a multilevel framework, allowing each of the four parameters to vary from participant to participant. Further details including priors and full code can be found with [ 7 ].…”

“…One weakness of the foraging model by Clarke et al (2022) [ 7 ] is that it makes little attempt to predict which item will be selected first. In this section we aim to improve this by modelling participant bias (or preference) in their choice of initial target selection.…”

“…These summary statistics can provide a broad view of switching behaviour, but they can also be biased by the spatial distribution of target types, and by a forager’s preference for one target or another. To address the need for a more precise set of measurements, we recently developed a new model to analyse foraging data, based on a sampling without replacement procedure [ 7 ]. By using this model, we demonstrated that we were able to break down foraging into a number of different cognitive biases, such as a preference to stick to the same target type, or a preference for nearby targets, and used this model to successfully reanalyse data from a number of open access datasets [ 2 , 8 , 9 , 10 ].…”