A Neural Model for Bayesian Computations in the Brain: From Optimal Information Encoding to Inference and Sampling Alessandro Ticchi 1 , A. Aldo Faisal 1,2 1 Dept of Computing, 2 Dept of Bioengineering, Imperial College London, UK Experimental evidence at the behavioural-level shows that brain make Bayes optimal decisions 1,2 , yet at the circuit level little is known experimentally about how brains may implement simulatenously Bayesian learning and inference (but see 3 ). Here we show how wiring anatomy and local synaptic learning rules can work together with molecular sources of noise 4-6 enabling populations of neurons to unify three features of Bayesian computations: a) simple local learning rules enable our model to learn optimal statistical representations of sensory information (as per 7 ). b) In absence of novel sensory information, the ubiquitous ion channel noise in neurons drives our model to autonomously produce samples from learned sensory input distributions i.e. representing the prior (consistent with data by 3 ) and c) local diffusive signals (e.g. nitric oxide) or recurrent wiring patterns suffice to enable our model to integrate any new information with the internally represented prior, thereby implementing a Markov Chain Monte Carlo sampling process which reflects inferred posterior distributions. Our model simulations in Figure 1-3 show a population of 20 stochastic neurons and demonstrate the 3 above features, by a) learning sensory tuning curves for the population in good agreement to theoretically derived optimal ones 7 (Figure 1-2, R 2 value >0.9 for density, weight of tuning curves), b) generating samples from learned prior distributions without sensory information and c) correctly computing posterior distributions with incoming sensory information (Figure 3, KL-divergence between model and analytically distributions <0.001). Specifically we tried a broad range of sensory input distributions from Gaussian, uniform to complex bi-modal distributions, achieving consistent results. In achieving these global behaviours microscopic noise, that represents a fundamental problem for information processing in brain, plays an unexpected constructing role, as it allows to get in correspondence with the statistical properties of the environment.