Bayesian Inference in Epidemic Modelling: A Beginner's Guide

TL;DR

This paper introduces Bayesian inference and MCMC methods for parameter estimation in epidemic models, using the SIR model as an example, aimed at beginners in epidemiology and Bayesian statistics.

Contribution

It provides a self-contained, step-by-step guide to applying Bayesian methods to epidemic modeling, including likelihood derivation, prior specification, and MCMC implementation.

Findings

Demonstrates how to derive likelihood functions for epidemic models

Shows how to implement Metropolis-Hastings algorithm for parameter sampling

Provides practical guidance for beginners in Bayesian epidemiology

Abstract

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.