The organization of the human brain is the result of multiple embedded evolutions, an ad hoc "bricolage" (Jacob, 1977) of the most diverse systems selected for their survival value, with no guarantee of optimality. This is why many neurobiologists and cognitive psychologists believe that there can be no universal mathematical theory of the brain, only restricted models of specific cognitive skills. Contrary to this widespread belief, however, a vast recent trend in cognitive science has been to use the mathematical theory of Bayesian inference to model a very wide range of psychological phenomena: perception, statistical inference, decision-making, learning, language processing and so on. The speed with which this theory is invading and unifying various fields of cognition, the simplicity of its axiomatic foundations, and the depth of its conclusions justify speaking of a veritable "Bayesian revolution" in cognitive science. The aim of the 2012 lecture was to explain its principles.
In a nutshell, Bayesian theory provides a mathematical model of the optimal way to conduct plausible reasoning in the presence of uncertainty. From birth, the baby seems to be endowed with skills for this kind of probabilistic reasoning. Bayesian inference also provides a good account of perceptual processes: given ambiguous inputs, the brain reconstructs the most likely interpretation. Bayes' rule shows how to optimally combine the a priori information from our evolution or memory with the data received from the outside world. In this way, it offers a new vision of learning that goes beyond the classic dilemma between empiricist and nativist theories. Finally, many human decisions seem to result from an approximation of the Bayesian rule of evidence accumulation, combined with an estimate of the expected value of the consequences of our choices. Insofar as the principles of Bayesian inference are thus shared by multiple domains of cognition, it could be that the architecture of the cortex has evolved to approximate this type of probabilistic computation at high speed and in a massively parallel fashion. The algorithm used could explain not only the layered organization of the cortex, but also the way our brains anticipate the outside world (predictive coding) and respond to novelty (propagation of error signals).