Bayesian Forecasting of Global Earthquakes (1918–2020)

This project uses Bayesian autoregressive models to forecast the annual count of worldwide earthquakes (magnitude > 7) using data from the USGS. The analysis focuses on a standalone AR(3) model with posterior inference, model order selection, and forecasting. The report also includes theoretical comparison with a mixture of AR(3) models.

🧠 Methods

• Model: AR(3) with Normal-Inverse Gamma conjugate prior
• Inference: Posterior sampling with 5000 draws in R
• Model order selection using PACF, AIC, and BIC
• Prior sensitivity analysis on hyperparameters

🔍 Note: While the accompanying report includes discussion of a mixture of AR(3) models and their DIC-based comparison, the current codebase implements only the standalone AR(3) analysis and forecasting pipeline.

📈 Results

• AR(3) model selected via PACF and AIC/BIC
• Posterior inference shown to be robust to prior hyperparameters
• Forecasts for 2021–2024: 12, 10, 10, 11 earthquakes

📂 Project Structure

• R/: Scripts for model order selection, prior sensitivity analysis, and prediction
• data/: Earthquake count data (taken from USGS website)
• results/: Saved plots and intermediate outputs (PACF, AIC/BIC)
• report/: PDF capstone report written in Overleaf

📌 Key Takeaways

• Demonstrates practical application of Bayesian time series modeling in R
• Implements MCMC-based posterior estimation with uncertainty quantification
• Uses real-world geophysical data in a forecasting context

📚 Tools Used

• R (version 4.x)
• Key packages: mvtnorm, MASS, stats, base

🧩 Planned Improvements

• Add inline comments to R scripts for better readability
• Reproduce missing mixture model code (optional)
• Convert scripts into R Markdown notebooks (optional)

Install required packages with:

install.packages(c("mvtnorm", "MASS"))