A Bayesian Sparse Generalized Linear Model With an Application to Multiscale Covariate Discovery for Observed Rainfall Extremes Over the United States

Abstract

Predictive insights on extreme and rare events are important across multiple disciplines ranging from hydrology, climate, and remote sensing to finance and security. Characterizing the dependence of extremes on covariates can help in identification of plausible causal drivers and may even inform predictive modeling. However, despite progress in the incorporation of covariates in the statistical theory of extremes and in sparse covariate discovery algorithms, progress has been limited for high-dimensional data where the number of covariates is large. In this paper, we propose a general-purpose sparse Bayesian framework for covariate discovery based on a Poisson description of extremes frequency and a hierarchical Bayesian description of a sparse regression model. We obtain posteriors over regression coefficients, which indicate dependence of extremes on the corresponding covariates, using a variational Bayes approximation. Experiments with synthetic data demonstrate the ability of the approach to accurately characterize dependence structures. The method is applied to discover the covariates affecting the frequency of precipitation extremes obtained from station-level observations over nine climatologically homogeneous regions within the continental U.S. The candidate covariates at multiple spatial scales represent station-level as well as regional and seasonal atmospheric condition, indices that attempt to capture large-scale ocean-based climate oscillators and hence natural climate variability, as well as global warming. Our results confirm the dependence structures that may be expected from known precipitation physics and generate novel insights, which can inform physical understanding and perhaps even predictive modeling.