Explore the core concepts of Bayesian methods and the implementation of Bayes' theorem and methods in machine learning. Examine Bayesian statistics and analysis with a focus on probability distribution and prior knowledge distribution.

describe the concept of Bayesian probability and statistical inference

describe the concept of Bayes' theorem and its implementation in machine learning

identify the role of probability and statistics in Bayesian analysis from the perspective of frequentist and subjective probability paradigms

describe standard probability, continuous, and discrete distribution

recall the essential ingredients of Bayesian statistics including prior distribution, likelihood function, and posterior inference

recognize the implementation of prominent Bayesian methods including inference, statistical modeling, influence of prior belief, and statistical graphics

identify the core concepts of Bayesian machine learning from the perspective of modeling, sampling algorithms, and variation inference

describe prior knowledge and compare the differences between non-informative prior distribution and informative prior distribution

recall the steps involved in Bayesian analysis, including modeling data, deciding prior distribution, likelihood construction, and posterior distribution

specify the essential ingredients of Bayesian statistics and recall the prominent Bayesian methods and the steps involved in Bayesian analysis