A central goal of neuroscience is to understand how learning is implemented by the nervous system. However, despite years of studies in animals and humans, our understanding of both the computational basis of learning and its implementation by the brain is still rudimentary. A critical gap therefore exists between the large amount of behavioral and neural data that has been collected during learning and a mathematical and biological understanding of the rules governing motor plasticity. This proposal will develop a unified mathematical theory for understanding how the brain learns complex skills. The theoretical framework will be implemented in software and will be applicable to and validated on a wide variety of sensorimotor data. The primary experimental validation system will be songbirds, which provide a physiologically accessible model system to investigate sensorimotor learning. Our objective in the songbird system is to understand sensorimotor learning of a single acoustic parameter ? fundamental frequency (pitch) ? which is known to be precisely regulated by the songbird brain. Our central hypothesis is that learning is implemented as a Bayesian inference, and that the stochastic sampling of motor commands from the current Bayesian a priori distribution of outputs is coordinated by a network of neurons in the forebrain. Drawing on a large quantity of both theoretical and experimental results, two specific aims will test this hypothesis. The first aim will introduce an innovative new class of computational model in which the brain uses an iterative process of Bayesian inference to reshape behavior in response to sensory feedback. The models will be validated using population-averaged animal behavior. The second aim will analyze data recorded from individual animals and single neurons in behaving animals to identify the biological mechanisms underlying sensorimotor learning. Throughout, we will design, test, and make public software that will allow other members of the community to apply our novel tools to their own data. Our approach is innovative because it will provide a unified framework for understanding the results of a wide variety of behavioral and neural studies across both tasks and species. These studies are significant because a better understanding of the mechanisms underlying sensorimotor learning could aid in the design of rehabilitative strategies that exploit the plasticity of complex behavior.