The idea that perception is a form of unconscious inference dates to Hermann von Helmholtz in the 1860s. Modern computational neuroscience has made this intuition precise: the Bayesian brain hypothesis proposes that the brain maintains probabilistic models of the environment, combines prior expectations with sensory evidence according to Bayes' theorem, and acts to minimize prediction error. This framework unifies a remarkable range of phenomena — from visual illusions and multisensory integration to motor control, learning, and psychiatric disorders.
The hypothesis does not claim the brain performs exact Bayesian computation. Rather, it proposes that neural circuits implement efficient approximations to Bayesian inference, using algorithms such as predictive coding, variational inference, and message passing in hierarchical generative models.
Perception as Inference
Sensory signals are inherently ambiguous. The same retinal image is consistent with infinitely many three-dimensional scenes. The brain resolves this ambiguity by combining the sensory evidence (the likelihood) with prior knowledge about the structure of the world (the prior) to compute the most probable interpretation (the posterior).
Where p(scene | sensation) → Posterior belief about the external cause
p(sensation | scene) → Generative model (how scenes produce sensations)
p(scene) → Prior expectations about the world
This framework explains why perception is not a passive recording of sensory input but an active, constructive process. Visual illusions arise when the prior dominates a weak or ambiguous likelihood. The hollow mask illusion — in which a concave face appears convex — reflects the brain's powerful prior that faces are convex objects. The Bayesian framework predicts that this illusion should weaken when the likelihood is strong (close viewing, stereoscopic depth cues), and it does.
Predictive Coding
Predictive coding is the most influential neural implementation of the Bayesian brain hypothesis. Proposed by Rao and Ballard (1999) and elaborated by Karl Friston and colleagues, it proposes that cortical circuits implement a hierarchical generative model in which each level predicts the activity of the level below.
At each level of the cortical hierarchy, neurons encode predictions about the expected input from the level below. These predictions are sent downward via feedback connections. The level below computes the prediction error — the difference between the prediction and the actual input — and sends this error signal upward via feedforward connections. Higher levels then update their representations to reduce the prediction error. The process iterates until the predictions match the input as closely as possible, at which point the system has found the most probable explanation of the sensory data.
μ̇ = D·μ + Σ_p · ∂g/∂μ · Σ_e⁻¹ · ε (state update)
Where μ → Expected hidden states (brain's "belief")
g(μ) → Predicted sensory input given current belief
ε → Prediction error signal
Σ_p, Σ_e → Prior and sensory precision (inverse variance)
The Free Energy Principle
Karl Friston's free energy principle (FEP) generalizes the Bayesian brain hypothesis into a unified theory of brain function — and, more ambitiously, of self-organizing biological systems in general. The principle states that all adaptive systems minimize an information-theoretic quantity called variational free energy, which bounds the surprise (negative log evidence) of their sensory observations.
= D_KL(q(θ) ‖ p(θ|y)) − ln p(y)
≥ −ln p(y)
Where q(θ) → Approximate posterior (the brain's current belief)
p(y, θ) → Generative model (joint distribution over data and causes)
D_KL → KL divergence between approximate and true posterior
−ln p(y) → Surprise (self-information of the sensory data)
Minimizing free energy with respect to the internal states (beliefs) is equivalent to approximate Bayesian inference — it makes q(theta) as close as possible to the true posterior p(theta|y). Minimizing free energy with respect to action — changing sensory input by moving, looking, or reaching — is equivalent to acting to confirm predictions and avoid surprising observations. This dual aspect unifies perception (updating beliefs) and action (changing the world) under a single objective.
Empirical Evidence
Multisensory Integration
When visual and auditory cues about the location of an object conflict, humans combine them in a manner closely matching the Bayesian optimal: each cue is weighted by its precision (inverse variance), and the combined estimate is more precise than either cue alone. This has been demonstrated in the ventriloquist effect and visual-haptic integration experiments by Ernst and Banks (2002).
Sensorimotor Control
Reaching movements show signatures of Bayesian inference. When visual feedback about hand position is uncertain, the motor system relies more on proprioceptive (body-sense) information, and vice versa. The precision-weighted combination of cues produces motor behavior that minimizes endpoint variability — exactly as a Bayesian controller would.
Neural Correlates
Mismatch negativity — an EEG/MEG signal evoked by unexpected stimuli — is naturally interpreted as a prediction error signal. Repetition suppression (reduced neural responses to repeated stimuli) reflects increasingly accurate predictions. The laminar structure of cortex, with distinct feedforward and feedback pathways, is architecturally consistent with predictive coding.
"The brain is fundamentally an organ of prediction, not reaction. Perception, action, and learning are all manifestations of the same underlying process: minimizing the discrepancy between what the brain expects and what it observes." — Karl Friston, "The free-energy principle: a unified brain theory?" (2010)
Computational Psychiatry
The Bayesian brain framework has generated a new field: computational psychiatry. Aberrant precision weighting — giving too much or too little weight to prediction errors — provides a unifying account of symptoms across several disorders. In autism, excessive sensory precision may explain hypersensitivity and difficulty with uncertain social cues. In schizophrenia, reduced precision on predictions may lead to the experience of unexpected, externally attributed events — hallucinations and delusions.
The Bayesian brain hypothesis is not universally accepted. Critics argue that the free energy principle, in its most general form, is unfalsifiable — any behavior can be described as free energy minimization under some generative model. Others question whether neural circuits actually implement probabilistic computations or merely approximate them in ways that happen to look Bayesian. Despite these debates, the framework has been extraordinarily productive, generating testable predictions and unifying disparate empirical findings across perception, action, and learning.
Active Inference
Active inference extends the free energy framework from perception to action. An agent minimizes expected free energy not only by updating beliefs (perception) but also by selecting actions that will generate the least surprising sensory data — or, equivalently, actions that will resolve uncertainty about the hidden states of the world. This dual objective — exploiting known rewards while exploring to reduce uncertainty — provides a principled solution to the exploration-exploitation tradeoff and connects the Bayesian brain to decision theory and reinforcement learning.