Recent researches point out the importance of the fast-slow cognitive process and learning process of self-body. Bayesian perspectives on the cognitive system also attract research attentions. The view of fast-slow dynamical system has long attracted wide range of attentions from physics to the neurobiology. In many research fields, there is a vast well-organized and coherent behavior in the multi degrees-of-freedom. This behavior matches the mathematical fact that fast-slow system is essentially described with a few variables. In this paper, we review the mathematical basis for understanding the fast-slow dynamical systems. Additionally, we review the basis of Bayesian statistics and provide a fast-slow perspective on the Bayesian inference.
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