The Bayesian Theory and Methods course aims to systematically teach the fundamental principles, main models, and commonly used algorithms of Bayesian statistics. The course starts with the basics of Bayes' theorem and gradually delves into more complex Bayesian inference and applications. Through theoretical learning and practical case analysis, students will fully grasp the application of Bayesian statistical methods in data analysis and inference. The course content includes fundamental concepts of Bayesian statistics as well as important topics such as Bayesian estimation, conjugate prior distributions, Bayesian hypothesis testing, and Bayesian decision theory. Additionally, the course will introduce common Bayesian computational methods, such as Markov Chain Monte Carlo (MCMC), Gibbs sampling, and variational inference, and explore the application of Bayesian methods in modern data science. This course emphasizes not only the transmission of theoretical knowledge but also practical operations. Students will use R and other statistical software to conduct data analysis and model building, mastering the practical application skills of Bayesian methods. The course design includes extensive case analysis and practical sessions, covering fields such as medicine, finance, engineering, and natural language processing. These elements help students apply theoretical knowledge to real-world problems, enhancing their comprehensive analysis and problem-solving abilities. |
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