Efficient behavior in our noisy and ambiguous world calls for the strategic use of the arising uncertainty by probabilistic inference [1]. Probabilistic inference in complex dynamic environments is challenging as it requires tracking not only individual latent variables but also the interactions among them. As a result, a neural circuit that optimally encodes these variables would need to be recurrently wired to relay information between them via feedback connections [2]. Given the additional cost of evolving and maintaining these feedback connections, we sought the circumstances under which the brain could get away with simpler circuits lacking some of the feedback connections necessary for optimal inference. One example of inference in a dynamic environment is navigation, in which self-motion and landmark cues inform estimates of our velocity and position in space, respectively [3]. As one’s velocity and position are coupled by kinematics, information about velocity can be used to improve the inference of position and vice versa, as predicted by optimal inference. Whereas animals are known to integrate self-motion cues to estimate their position [4, 5], it remains unclear whether animals use successive observations of position landmarks to infer their velocity. To assess the implication of a potential feedback connection relaying position information to velocity-coding brain areas, we developed a mathematical framework that allows us to compare the performance of an optimal inference algorithm to one where feedback from position to velocity is lacking. We found that an algorithm lacking such feedback only causes non-negligible performance loss if landmark observations are reliable but self-motion observations are unreliable. We further found that this performance deficit is, in fact, negligible at most biologically realistic noise levels. Thus, a heuristic algorithm without all the necessary components for optimal inference could nevertheless support efficient navigation at lower developmental and metabolic costs. Moreover, our mathematical framework can be extended beyond spatial navigation to examine the role that interactions between latent variables play in other neural computations.