Inference on Climate Indices Using Bayesian Variable Selection in Quantile Regression

Abstract

Rainfall variability significantly affects ecosystems, agriculture, and water management in eastern Australia. Influenced by global climate phenomena, these fluctuations challenge management practices at different locations and times of the year. Understanding these drivers is essential to improve resource management and mitigate the impacts of extreme weather events such as droughts and floods. Advancements in physical and statistical climate models have enhanced our understanding of global climate phenomena in relation to daily rainfall extremes. However, these models often lack a probabilistic framework that can assess the relationship between climate drivers and the full distribution of monthly rainfall. A key challenge is the inadequate modeling of uncertainty and variability inherent in climate systems. Bayesian approaches with variable selection are valuable in this context, as they incorporate prior knowledge and provide robust parameter estimation. Nonetheless, applications of such models that comprehensively assess the relationship between climate indices and the full distribution of monthly rainfall—including extremes—remain limited. This gap highlights the need for further development to improve predictive capabilities for monthly rainfall patterns under varying climate conditions. This thesis introduces a novel approach that employs Bayesian variable selection within a spatial quantile regression framework to examine the relationship between global climate indices and monthly rainfall distribution in New South Wales (NSW), Australia. By analyzing different quantiles of rainfall, this approach aims to offer a spatially varying inference of how these climate indices impact the entire spectrum of rainfall. This approach utilizes a hierarchical Bayesian quantile regression model to address distinct modeling requirements and complexities at each hierarchical level.