This chapter is a succinct introduction to basic probabilistic methods for pattern recognition and machine learning. One focus is to clearly present the exact meanings of different terms, including the taxonomy of different probabilistic methods. We present a basic introduction to maximum likelihood and maximum a posteriori estimation, and a very brief example to showcase the concept of Bayesian estimation. For the nonparametric world, we start from the drawbacks of parametric methods, gradually analyzing the properties preferred for a nonparametric one, and finally reach the kernel density estimation, a typical nonparametric method.
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