This lecture note provides a self-contained introduction to Bayesian inference and Markov Chain Monte Carlo (MCMC) methods for parameter estimation in epidemic models. Using the classical Susceptible-Infectious-Recovered (SIR) compartmental model as a running example, we derive the likelihood function from first principles, specify priors on the transmission and recovery parameters, and implement the Metropolis-Hastings algorithm to sample from the posterior distribution. The note is aimed at graduate students and researchers in mathematical epidemiology with limited prior exposure to Bayesian statistics.

翻译：本讲义为流行病学模型中的参数估计问题，提供了自成体系的贝叶斯推断与马尔可夫链蒙特卡洛（MCMC）方法入门指南。以经典的易感-感染-恢复（SIR）仓室模型作为贯穿始终的示例，我们从基本原理出发推导似然函数，对传播参数与恢复参数设定先验分布，并实现Metropolis-Hastings算法以从后验分布中采样。本讲义主要面向数学流行病学领域、先前贝叶斯统计学基础有限的研究生与科研人员。