Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Bayesian Inference in Epidemic Modelling: A Beginner's Guide

Augustine Okolie

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.

Bayesian Inference in Epidemic Modelling: A Beginner's Guide

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.
Paper Structure (22 sections, 14 equations, 2 figures, 1 table)

This paper contains 22 sections, 14 equations, 2 figures, 1 table.

Table of Contents

  1. Why Do We Need Bayesian Inference?
  2. The SIR Model
  3. Solving the ODE: From Equations to Epidemic Curves
  4. Interpreting the SIR Dynamics
  5. Bayesian Inference Setup
  6. Specifying the Likelihood
  7. The noise model
  8. Deriving the log-likelihood
  9. Specifying the Prior
  10. Markov Chain Monte Carlo (MCMC)
  11. The core idea
  12. The Metropolis-Hastings Algorithm
  13. Why does this work?
  14. Burn-in
  15. MCMC Results and Discussion
  16. ...and 7 more sections

Figures (2)

  • Figure 1: Numerical solution of the SIR model. $N=1000$, $I(0)=10$, $S(0)=990$, $R(0)=0$, with $\beta=0.3$, $\gamma=0.1$, $\mathcal{R}_0=3.0$.
  • Figure 2: MCMC output for the SIR parameter estimation problem ($N=1000$, $\beta^*=0.3$, $\gamma^*=0.1$, $\mathcal{R}_0^*=3.0$, 8000 iterations, burn-in = 2000). Top row, left to right: noisy observed infected counts against the true epidemic curve; MCMC trace for $\beta$; MCMC trace for $\gamma$. Bottom row, left to right: posterior distribution of $\beta$; posterior distribution of $\gamma$; posterior predictive check showing 100 SIR trajectories drawn from the posterior against the observed data.