Do Bayesianists strongly believe that the Bayes' theorem accurately describes how the brain changes its latent variables in face of new data? It seems very unlikely to me that the brain keeps track of probability distributions and that they sum up to one. How do Bayesianists believe this works at the neuronal level?
The term you will want to use in your Google search is "Bayesian cognitive science". It's a huge field. But the short answer is, yes, the people in that field do assume that the brain does something that can be modelled as keeping and updating a probability distribution according to Bayes' rule. Much of it is computational-level modelling, i.e. rather removed from questions of implementation in the brain. A quick Google search did, however, find some papers on how to implement Bayesian inference in neural networks - though not necessarily linked to the brain. I'm sure some people do the latter sort of thing as well, though.
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