Bayesian combination of two-dimensional location estimates

Friedman, Alinda; Ludvig, Elliot Andrew; Legge, Eric L. G.; Vuong, Quoc C.

doi:10.3758/s13428-012-0241-x

Cited by 10 publications

(8 citation statements)

References 25 publications

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“…4A). If the more familiar view is associated with a more reliable directional signal (Wystrach and Graham, 2012), this pattern accords with Bayesian principles (Cheng et al, 2007;Friedman et al, 2013;Körding, 2007), at least qualitatively: the weight assigned to a cue is in accord with its reliability.…”

Section: Discussionmentioning

confidence: 64%

Combining sky and Earth: Desert ants (Melophorus bagoti) show weighted integration of celestial and terrestrial cues

Legge

Wystrach

Spetch

et al. 2014

Journal of Experimental Biology

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Insects typically use celestial sources of directional information for path integration, and terrestrial panoramic information for view-based navigation. Here we set celestial and terrestrial sources of directional information in conflict for homing desert ants (Melophorus bagoti). In the first experiment, ants learned to navigate out of a round experimental arena with a distinctive artificial panorama. On crucial tests, we rotated the arena to create a conflict between the artificial panorama and celestial information. In a second experiment, ants at a feeder in their natural visually-cluttered habitat were displaced prior to their homing journey so that the dictates of path integration (feeder to nest direction) based on a celestial compass conflicted with the dictates of view-based navigation (release point to nest direction) based on the natural terrestrial panorama. In both experiments, ants generally headed in a direction intermediate to the dictates of celestial and terrestrial information. In the second experiment, the ants put more weight on the terrestrial cues when they provided better directional information. We conclude that desert ants weight and integrate the dictates of celestial and terrestrial information in determining their initial heading, even when the two directional cues are highly discrepant.

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Section: Discussionmentioning

confidence: 64%

Combining sky and Earth: Desert ants (Melophorus bagoti) show weighted integration of celestial and terrestrial cues

Legge

Wystrach

Spetch

et al. 2014

Journal of Experimental Biology

Self Cite

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“…An important step for future research is to extend the models to the environments in which participants actually navigate. Friedman et al (2013) published an excellent tutorial on applications of the standard model to twodimensions, and in Appendix A we provide the derivation of Gaussian weighted squared-error loss in two dimensions (this derivation generalizes to the incorporation of a prior with individual spatial cues in two dimensions). A major benefit of extending the models to two dimensions is that formal models of single-cue likelihood functions (e.g., models that generate bivariate distributions of locations on the ground plane) can be developed and used to derive the posterior.…”

Section: Discussionmentioning

confidence: 99%

Bayesian decision theory and navigation

McNamara

Chen

2021

Psychon Bull Rev

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Spatial navigation is a complex cognitive activity that depends on perception, action, memory, reasoning, and problem solving. Effective navigation depends on the ability to combine information from multiple spatial cues to estimate one's position and the locations of goals. Spatial cues include landmarks, and other visible features of the environment, and body-based cues generated by self-motion (vestibular, proprioceptive, & efferent information). A number of projects have investigated the extent to which visual cues and body-based cues are combined optimally according to statistical principles. Possible limitations of these investigations are that they have not accounted for navigators' prior experiences with or assumptions about the task environment and have not tested complete decision models. We examine cue combination in spatial navigation from a Bayesian perspective and present the fundamental principles of Bayesian decision theory. We show that a complete Bayesian decision model with an explicit loss function can explain a discrepancy between optimal cue weights and empirical cues weights observed by Chen, McNamara, Kelly and Wolbers (2017) and that the use of informative priors to represent cue bias can explain the incongruity between heading variability and heading direction observed by Zhao and Warren (2015b). We also discuss Petzschner and Glasauer's (2011) use of priors to explain biases in estimates of linear displacements during visual path integration. We conclude that Bayesian decision theory offers a productive theoretical framework for investigating human spatial navigation and believe that it will lead to a deeper understanding of navigational behaviors.

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“…An important step for future research is to extend the models to the environments in which participants actually navigate. Friedman et al (2013) published an excellent tutorial on applications of the MLE model to two-dimensions, and in Appendix D we provide the derivation of Gaussian weighted squared-error loss in two dimensions (this derivation generalizes to the incorporation of a prior with individual spatial cues in two dimensions). A major benefit of extending the models to two dimensions is that formal models of single-cue likelihood functions (e.g., models that generate bivariate distributions of locations on the ground plane) can be developed and used to derive the posterior.…”

Section: Several Projects Have Investigated Cue Combination In Navigamentioning

confidence: 99%

Bayesian Decision Theory and Navigation

McNamara¹,

Chen²

2020

Preprint

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Spatial navigation is a complex cognitive activity that depends on perception, action, memory, reasoning, and problem solving. People rely on their navigational skills every day, from activities as common as getting from home to work and back again, to less routine endeavors, such as finding a tourist destination in an unfamiliar city. Effective navigation depends on the ability to combine information from multiple spatial cues to estimate one's position and the locations of goals. Spatial cues include landmarks, and other visible features of the environment, and body-based cues generated by selfmotion (vestibular, proprioceptive, & efferent information). A number of projects have investigated the extent to which visual cues and body-based cues are combined optimally according to statistical principles. Although several studies have documented optimal or near-optimal cue combination, other studies have shown that navigators sometimes fail to combine cues optimally or even at all. Possible limitations of all of these investigations are that they have not accounted for navigators' prior experiences with or assumptions about the task environment and have not tested complete decision models. We show that some apparent violations of optimal cue combination can be explained by incorporating informative Bayesian priors or appropriate loss functions in decision-theoretic models, and propose novel lines of research on human spatial navigation that are motivated by Bayesian decision theory.

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Bayesian combination of two-dimensional location estimates

Cited by 10 publications

References 25 publications

Combining sky and Earth: Desert ants (Melophorus bagoti) show weighted integration of celestial and terrestrial cues

Combining sky and Earth: Desert ants (Melophorus bagoti) show weighted integration of celestial and terrestrial cues

Bayesian decision theory and navigation

Bayesian Decision Theory and Navigation

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