Spatiotemporal Quantile Regression for Detecting Distributional Changes in Environmental Processes

• Activity Number: 142
• Type: Invited
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Brian Reich*+
• Companies: North Carolina State University
• Keywords: Bayesian hierarchical model ; climate change ; non-Gaussian data ; US temperature data ; warming hole

Abstract

Climate change may lead to changes in several aspects of the distribution of climate variables, including changes in the mean, increased variability, and severity of extreme events. We propose using spatiotemporal quantile regression as a flexible and interpretable method for simultaneously detecting changes in several features of the distribution of climate variables. Unlike classical quantile regression which uses model-free methods to analyze a single quantile or several quantiles separately, we take a model-based approach which jointly models all quantiles, and thus the entire response distribution. In the spatiotemporal quantile regression model, each spatial location has its own quantile function that evolves over time, and the quantile functions are smoothed spatially using Gaussian process priors. We propose a basis expansion for the quantile function that permits a closed-form for the likelihood, and allows for residual correlation modeling via a Gaussian spatial copula. We illustrate the methods using temperature data for the southeast US from the years 1931-2009.