Fig. 3: A hierarchical generative model and posterior inference via Gibbs sampling.
From: Sampling-based Bayesian inference in recurrent circuits of stochastic spiking neurons
a An example of sensory feedforward input generation: The stimulus parameter, z, is the orientation of the tree trunk, and the stimulus, s, is the orientation of the bark texture located in the classical receptive field of a V1 hypercolumn. The recurrent circuit generates samples from the joint posterior over stimulus and stimulus parameter. Solid circles: observations and responses in the brain; dashed circles: latent variables in the external world. Nature image is adapted from Tkačik, G. et al. Natural images from the birthplace of the human eye. PLoS one 6, e20409 (2011). b The joint prior over the stimulus parameter, z, and stimulus, s, is concentrated on the diagonal. The correlation between context and stimulus is determined by parameter Λs. (c) The posterior over stimulus parameter and stimulus can be approximated via Gibbs sampling (Eqs. (4a), (4c)) by iteratively generating samples of s and z from their respective conditional distributions. d The resulting approximations of the joint and marginal posterior over s and z. Light blue contour: the posterior distribution (Eq. (24)); Red dots: Samples obtained using Gibbs sampling. The green and orange projections are the marginal posterior distributions of s and z, respectively.
