  Bayesian models of cognition hypothesize that human brains make sense of data
by representing probability distributions and applying Bayes' rule to find the
best explanation for available data. Understanding the neural mechanisms
underlying probabilistic models remains important because Bayesian models
provide a computational framework, rather than specifying mechanistic
processes. Here, we propose a deterministic neural-network model which
estimates and represents probability distributions from observable events --- a
phenomenon related to the concept of probability matching. Our model learns to
represent probabilities without receiving any representation of them from the
external world, but rather by experiencing the occurrence patterns of
individual events. Our neural implementation of probability matching is paired
with a neural module applying Bayes' rule, forming a comprehensive neural
scheme to simulate human Bayesian learning and inference. Our model also
provides novel explanations of base-rate neglect, a notable deviation from
Bayes.
