Efficient coding connects prior and likelihood function in perceptual Bayesian inference

A common challenge for Bayesian approaches in modeling perceptual behavior is the fact that the two fundamental components of a Bayesian model, the prior distribution and the likelihood function, are formally unconstrained. Here we argue that a neural system that emulates Bayesian inference naturally imposes constraints by way of how it represents sensory information in populations of neurons. More specifically, we propose an efficient encoding principle that constrains both the likelihood and the prior based on low-level environmental statistics. The resulting Bayesian estimates can show biases away from the peaks of a prior distribution, a behavior seemingly at odds with the traditional view of Bayesian estimates yet one that has indeed been reported in human perception of visual orientation. We demonstrate that our framework correctly predicts these biases, and show that the efficient encoding characteristics of the model neural population matches the reported orientation tuning characteristics of neurons in primary visual cortex. Our results suggest that efficient coding can be a promising hypothesis in constraining neural implementations of Bayesian inference.