Paper List

期刊: ArXiv Preprint
发布日期: 2026-03-16
EpidemiologyComputational Statistics

Bayesian Inference in Epidemic Modelling: A Beginner’s Guide Illustrated with the SIR Model

PhD Mathematics

Augustine Okolie
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IN SHORT: This guide addresses the core challenge of estimating uncertain epidemiological parameters (like transmission and recovery rates) from noisy, real-world outbreak data by providing a clear, applied pathway using Bayesian inference and MCMC.

核心创新

  • Methodology Presents an integrated, pedagogical pipeline from the SIR ODE model through Bayesian likelihood formulation to practical MCMC implementation, demystifying the process for beginners.
  • Methodology Explicitly connects the Gaussian noise assumption in the likelihood to the common least-squares fitting approach, framing Bayesian inference as its natural probabilistic extension with uncertainty quantification.
  • Theory Emphasizes the interpretative power of the full posterior distribution and credible intervals over single point estimates, highlighting this as the key advantage for decision-making under uncertainty.

主要结论

  • In a synthetic example with true parameters β=0.3, γ=0.1 (R0=3.0), MCMC recovered posterior means of β=0.300 (std 0.002) and γ=0.102 (std 0.001), demonstrating accurate and precise inference.
  • The posterior distribution for R0 was estimated as 2.95 with a standard deviation of 0.03, showing the method successfully quantifies uncertainty in this critical epidemiological metric.
  • The framework successfully separates the roles of individual parameters β and γ, showing that different pairs can yield the same R0 but produce distinct epidemic curve shapes (e.g., peak sharpness), which point estimates alone would miss.
研究空白： While compartmental models like SIR are widely used, a practical gap exists for beginners and practitioners in moving from model equations to robust, probabilistic parameter estimation that quantifies uncertainty, which is critical for real-world epidemic forecasting and intervention planning.

摘要: This guide provides a beginner-friendly introduction to Bayesian inference in the context of epidemic modeling, using the classic Susceptible-Infected-Recovered (SIR) model as a working example. It covers the mathematical setup of the SIR ordinary differential equations, the formulation of the Bayesian inference problem (likelihood and prior specification), and the implementation of Markov Chain Monte Carlo (MCMC) via the Metropolis-Hastings algorithm to estimate transmission (β) and recovery (γ) rates from noisy outbreak data. The tutorial emphasizes the conceptual advantages of the Bayesian framework—which provides full posterior distributions quantifying parameter uncertainty—over frequentist point estimates, and walks through a complete synthetic example with results and interpretation.