UCSC-SOE-20-14: Fast inference for time-varying quantiles via flexible dynamic models with application to the characterization of atmospheric

Raquel Barata, Raquel Prado and Bruno Sanso
12/14/2020 04:11 PM
Atmospheric rivers (ARs) are elongated regions of water vapor in the at- mosphere that play a key role in global water cycles, particularly in western US 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 para- metric distributions for quantile regression, this paper develops a flexible dy- namic 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 para- metric quantile regression approach for non-standard distributions, perform- ing 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 approxi- mate 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 non-linear re- lationships 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 NiƱo Southern Oscillation Longitude Index on the estimation of the 0.85 quantile IVT.