Fast inference for time-varying quantiles via flexible dynamic models with application to the characterization of atmospheric rivers

Abstract

Atmospheric rivers (ARs) are elongated regions of water vapor in the atmosphere that play a key role in global water cycles, particularly in western U.S. precipitation. The primary component of many AR detection schemes is the thresholding of the integrated water vapor transport (IVT) magnitude at a single quantile over time. Utilizing a recently developed family of parametric distributions for quantile regression, this paper develops a flexible dynamic quantile linear model (exDQLM) which enables versatile, structured, and informative estimation of the IVT quantile threshold. A simulation study illustrates our exDQLM to be more robust than the standard Bayesian parametric quantile regression approach for nonstandard distributions, performing better in both quantile estimation and predictive accuracy. In addition to a Markov chain Monte Carlo (MCMC) algorithm, we develop an efficient importance sampling variational Bayes (ISVB) algorithm for fast approximate Bayesian inference which is found to produce comparable results to the MCMC in a fraction of the computation time. Further, we develop a transfer function extension to our exDQLM as a method for quantifying nonlinear relationships between a quantile of a climatological response and an input. The utility of our transfer function exDQLM is demonstrated in capturing both the immediate and lagged effects of El Niño Southern Oscillation Longitude Index on the estimation of the 0.85 quantile IVT.