Bayesian approaches to extreme value modeling, with applications to wildfires

Abstract

The growing frequency and size of wildfires across the US necessitates accurate quantitative assessment of evolving wildfire behavior to predict risk from future extreme wildfires. In Chapter 2, we build a joint model of wildfire counts and burned areas, regressing key model parameters on climate and demographic covariates. We use extended generalized Pareto distributions to model the full distribution of burned areas, capturing both moderate and extreme sizes, while leveraging extreme value theory to focus particularly on the right tail. We model wildfire counts using a zero-inflated negative binomial model and join the wildfire counts and burned areas sub-models via a temporally varying shared random effect. Our model successfully captures the trends of wildfire counts and burned areas. By investigating the predictive power of different sets of covariates, we find that fire indices are better predictors of wildfire burned area behavior than individual climate covariates, whereas climate covariates are influential drivers of wildfire occurrence behavior. Recent advances in multivariate extreme value modeling leverage a geometric perspective, using the shape of the multivariate point cloud and its connection to the Lebesgue joint density, to make inference on joint tail probabilities. While the original statistical framework was fully parametric, relying on a gauge function that uniquely defines the shape for a given density, newer methods have introduced semi- and non-parametric alternatives to increase flexibility. In Chapter 3, we propose a modeling approach that retains the simplicity of the parametric framework but adds flexibility by using Bayesian model averaging (BMA) to improve prediction of tail risk probabilities. In contrast to previous works that rely solely on a truncated radial likelihood, we propose using a censored likelihood, which we find consistently outperforms the truncated radial likelihood, particularly in small-sample settings. To generate predictions, we use a simple importance sampling scheme that matches the accuracy of more complex methods at a fraction of the computational cost. Finally, we apply our approach to two fire weather indices, which are designed to capture somewhat orthogonal aspects of fire risk, to illustrate the practical utility of our method in environmental applications.