I'm a mathematician by training and, for 30 years, a cognitive (neuro)scientist. I would have asked this question for the human mind rather than for the human brain, but I would say it's neither quantic not Bayesian, but Occamian. At least, my work on human visual perceptual organization suggests that it is guided by the simplicity of mental representations. This can, if desired, be translated in Bayesian terms, but then using probabilities that are inversely related to representational complexities. It is also corroborated by what I called transparallel processing to compute simplest representations of strings. I implemented this in an algorithm for single-processor classical computers, but notice that transparallel processing has the same computing power as that promised by quantum computers. I postulate that, in the brain, neuronal synchronization is a manifestation of transparallel processing. In this sense, I would say that quantic and Bayesian are nice ways to model (depending on your preference) the mind/brain, but that both ways are merely reflections of the Occamian mind/brain.

dear peter

thank you 

i do not know occamian brain

but you confirm my point of view

it depend of the observer

you are the third observer (the cognitive neuro scientist one) 

dear  eraldo

i agree.