Bayesian Models of Brain and Behaviour

Figure 3

Bayes rule for Gaussians. For the prior 𝑝(𝑥) (blue) 𝑚₀=20,𝜆₀=1 and the likelihood 𝑝(𝑦∣𝑥) (red) 𝑚_𝐷=25 and 𝜆_𝐷=3, the posterior 𝑝(𝑥∣𝑦) (magenta) shows the posterior distribution with 𝑚=23.75 and 𝜆=4. The posterior is closer to the likelihood than the prior because the likelihood has higher precision. Bayes rule for Gaussians has been used to explain many behaviours from sensory integration to collective decision making.