Enhancing Bayesian Approaches in the Cognitive and Neural Sciences via Complex Dynamical Systems Theory

In the cognitive and neural sciences, Bayesianism refers to a collection of concepts and methods stemming from various implementations of Bayes' theorem, which is a formal way to calculate the conditional probability of a hypothesis being true based on prior expectations and updating priors in the face of errors. Bayes' theorem has been fruitfully applied to describe and explain a wide range of cognitive and neural phenomena (e.g., visual perception and neural population activity) and is at the core of various theories (e.g., predictive processing). Despite these successes, we claim that Bayesianism has two interrelated shortcomings: its calculations and models are predominantly linear and noise is assumed to be random and unstructured versus deterministic. We outline ways that Bayesianism can address those shortcomings: first, by making more central the nonlinearities characteristic of biological cognitive systems, and second, by treating noise not as random and unstructured dynamics, but as the kind of structured nonlinearities of complex dynamical systems (e.g., chaos and fractals). We provide bistable visual percepts as an example of a real-world phenomenon that demonstrates the fruitfulness of integrating complex dynamical systems theory in Bayesian treatments of perception. Doing so facilitates a Bayesianism that is more capable of explaining a number of currently out-of-reach natural phenomena on their own, biologically realistic terms.