Bayesian Decision Theory and Navigation

Abstract

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.

A Dynamic Bayesian Actor Model explains Endpoint Variability in Homing Tasks

“…Analysis of regression coefficients shows intercepts larger than zero and slopes less than one, indicating a regression to the mean (poor environment: R 2 = 0.361, p = 0.011, slope 95% ci (0.099, 0.636); rich environment: R 2 = 0.45, p = 0.003, slope 95% ci (0.195, 0.804)). According to the cue integration interpretation [39, 44], subjects underweighted the influence of self-motion cues and overweighted the influence of landmark cues, as measured by the response variability in both single cue conditions.…”

“…Here, we hypothesized that such seemingly sub-optimal ‘cue weights’ arise as optimal actions under perceptual, motor, and representational uncertainties from the perspective of our dynamic Bayesian actor model, rather than making additional assumptions about cost-functions, penalizing responses deviating from the mid-point between the two cues in to correct these see mingly sub-optimal ‘cue weights’ [44]. Based on response variability (shown in Figure 5C-D) and mean responses in conflict conditions (shown in Figure 6A; right) we computed both types of ‘cue weights’ in the two environments, replicating the analysis from Chen 2017 [39] for virtual subjects from our computational model Figure 6B.…”

“…A popular family of tasks that have been used to investigate the contributions of different sources of information to spatial navigation behavior are triangle-completion (or homing) tasks [3]. While prior research has shown that humans are able to combine different spatial cues and thereby reduce their navigational variability [34, 35, 37, 39–41, 44, 59, 60], it is still unclear how or why the observed variability in trajectories and endpoints arises and how path-integration and landmark cues interact in this process, which necessarily requires recurring to a computational model.…”

“…We adopt the notation by McNamara 2021 [44] to describe ideal observer analysis for the homing task. Subjects infer a target’s location L , given self-motion S and visual landmark cues V .…”

“…As an example, for cue conflicts due to large landmark rotations, a single cue may determine the response direction, but response variability was reduced at the same time [38,43], while for small landmark rotations, the response direction was biased toward the pathintegration cue [39]. A recent study [44] suggested accounting for discrepancies to Bayesian cue integration by postulating a strong prior over target locations and additional behavioral costs but still framing the task as perceptual cue integration. However, cue integration models are ideal observer models [45], i.e., they are purely perceptual and do not incorporate uncertainty in either motor actions [46] or internal models [27].…”