An increasing number of experimental studies indicate that perception encodes a posterior probability distribution over possible causes of sensory stimuli, which is used to act close to optimally in the environment. One outstanding difficulty with this hypothesis is that the exact posterior will in general be too complex to be represented directly, and thus neurons will have to represent an approximation of this distribution. Two influential proposals of efficient posterior representation by neural populations are: 1) neural activity represents samples of the underlying distribution, or 2) they represent a parametric representation of a variational approximation of the posterior. We show that these approaches can be combined for an inference scheme that retains the advantages of both: it is able to represent multiple modes and arbitrary correlations, a feature of sampling methods, and it reduces the represented space to regions of high probability mass, a strength of variational approximations. Neurally, the combined method can be interpreted as a feed-forward preselection of the relevant state space, followed by a neural dynamics implementation of Markov Chain Monte Carlo (MCMC) to approximate the posterior over the relevant states.

An increasing number of experimental studies indicate that perception encodes a posterior probability distribution over possible causes of sensory stimuli, which is used to act close to optimally in the environment. One outstanding difficulty with this hypothesis is that the exact posterior will in general be too complex to be represented directly, and thus neurons will have to represent an approximation of this distribution. Two influential proposals of efficient posterior representation by neural populations are: 1) neural activity represents samples of the underlying distribution, or 2) they represent a parametric representation of a variational approximation of the posterior. We show that these approaches can be combined for an inference scheme that retains the advantages of both: it is able to represent multiple modes and arbitrary correlations, a feature of sampling methods, and it reduces the represented space to regions of high probability mass, a strength of variational approximations. Neurally, the combined method can be interpreted as a feed-forward preselection of the relevant state space, followed by a neural dynamics implementation of Markov Chain Monte Carlo (MCMC) to approximate the posterior over the relevant states.