Spatial Quantile Regression Method Based On Gibbs Algorithm And Its Application

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.In this paper,we propose using Gibbs algorithm quantile regression as a flexible and interpretable method for simultaneously detecting changes in several features of the distribution of climate variables.The Gibbs algorithm quantile regression model assumes that each quantile level changes linearly in time,permitting straight-forward inference on the time trend for each quantile level.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 Gibbs algorithm 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 China from the years 2005-2015.For these data,borrowing information across space identifies more significant time trends than classical non-spatial quantile regression.We find a decreasing time trend for much of the spatial domain for monthly mean and minimum temperatures.For the lower quantiles of monthly minimum temperature,we find a decrease in the northeast,and an increase mean temperature in Hebei...