This paper presents a review of Bayesian models of brain and behaviour. We first review the basic principles of Bayesian inference. This is followed by descriptions of sampling and variational methods for approximate inference, and forward and backward recursions in time for inference in dynamical models. The review of behavioural models covers work in visual processing, sensory integration, sensorimotor integration, and collective decision making. The review of brain models covers a range of spatial scales from synapses to neurons and population codes, but with an emphasis on models of cortical hierarchies. We describe a simple hierarchical model which provides a mathematical framework relating constructs in Bayesian inference to those in neural computation. We close by reviewing recent theoretical developments in Bayesian inference for planning and control. 1. Introduction This paper presents a review of Bayesian models of brain and behaviour. Overall, the aim of the paper is to review work which relates constructs in Bayesian inference to aspects of behaviour and neural computation, as outlined in Figure 1. This is a very large research area and we refer readers to standard textbooks and other review materials [1–6]. Figure 1: This paper reviews work which relates constructs in Bayesian inference to those in experimental psychology and neuroscience. One of the main ideas to emerge in recent years is that Bayesian inference operates at the level of cortical macrocircuits. These circuits are arranged in a hierarchy which reflects the hierarchical structure of the world around us. The idea that the brain encodes a model of the world and makes predictions about its sensory input is also known as predictive coding [7]. Consider, for example, your immediate environment. It may be populated by various objects such as desks, chairs, walls, trees, and so forth. Generic attributes of this scene and the objects in it will be represented by activity in brain regions near the top of the hierarchy. The connections from higher to lower regions then encode a model of your world, describing how scenes consist of objects, and objects by their features. If a higher level representation is activated, it will activate those lower level representations that encode the presence of, for example, configurations of oriented lines that your brain expects to receive signals about in early visual cortex. At the lowest level of the hierarchy these predictions are compared with sensory input and the difference between them, the prediction error, is propagated back up the
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