To localize ourselves in an environment for spatial navigation, we rely on vision and self-motion inputs, which only provide noisy and partial information. It is unknown how the resulting uncertainty affects navigation behavior and neural representations. Here we show that spatial uncertainty underlies key effects of environmental geometry on navigation behavior and grid field deformations. We develop an ideal observer model, which continually updates probabilistic beliefs about its allocentric location by optimally combining noisy egocentric visual and self-motion inputs via Bayesian filtering. This model directly yields predictions for navigation behavior and also predicts neural responses under population coding of location uncertainty. We simulate this model numerically under manipulations of a major source of uncertainty, environmental geometry, and support our simulations by analytic derivations for its most salient qualitative features. We show that our model correctly predicts a wide range of experimentally observed effects of the environmental geometry and its change on homing response distribution and grid field deformation. Thus, our model provides a unifying, normative account for the dependence of homing behavior and grid fields on environmental geometry, and identifies the unavoidable uncertainty in navigation as a key factor underlying these diverse phenomena.

The assumed data generating models (response distributions) of experimental or observational data in cognitive science have become increasingly complex over the past decades. This trend follows a revolution in model estimation methods and a drastic increase in computing power available to researchers. Today, higher-level cognitive functions can well be captured by and understood through computational cognitive models, a common example being drift diffusion models for decision processes. Such models are often expressed as the combination of two modeling layers. The first layer is the response distribution with corresponding distributional parameters tailored to the cognitive process under investigation. The second layer are latent models of the distributional parameters that capture how those parameters vary as a function of design, stimulus, or person characteristics, often in an additive manner. Such cognitive models can thus be understood as special cases of distributional regression models where multiple distributional parameters, rather than just a single centrality parameter, are predicted by additive models. Because of their complexity, distributional models are quite complicated to estimate, but recent advances in Bayesian estimation methods and corresponding software make them increasingly more feasible. In this talk, I will speak about the specification, estimation, and post-processing of Bayesian distributional regression models and how they can help to better understand cognitive processes.