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.

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