This notebook demonstrates the complete workflow for building a Bayesian Simple Linear Regression model using PyMC to predict wildfire sizes solely from wind speed data. In it we formalize the model using statistical notation, implement prior predictive simulations to validate our assumptions, and then generate posterior distributions through Markov Chain Monte Carlo (MCMC) sampling. Unfortunately, the analysis revealed that wind speed alone is a weak (quite honestly, a terrible) predictor of fire size. Nonetheless, the value-add in our work was that it provided practical insights about the importance of model diagnostics and the pitfalls of violating assumptions of linearity and heteroscedasticity when working with real-world data!

Topics covered:

• Statistical model notation for Bayesian Linear Regression (priors, likelihood, parameters)
• Log transformations to handle right-skewed distributions
• Prior predictive simulation to validate parameter choices
• PyMC implementation with Normal and HalfNormal distributions
• MCMC sampling to generate posterior distributions
• Model evaluation through trace plots and regression line uncertainty
• Diagnosing assumption violations (homoscedasticity, linearity, heteroscedasticity)

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