Advancement: Flexible Dynamic Quantile Linear Models

Speaker Name: 
Raquel Barata
Speaker Title: 
PhD Student (Advisor: Bruno Sanso and Raquel Prado)
Speaker Organization: 
Statistics & Applied Mathematics
Start Time: 
Friday, October 12, 2018 - 11:00am
End Time: 
Friday, October 12, 2018 - 1:00pm
Location: 
Baskin Engineering, Room 330
Organizer: 
Bruno Sanso and Raquel Prado

Abstract:  Atmospheric rivers (ARs) play a key role in the global water cycle and regional weather. To understand the representation of ARs in global climate and weather models several techniques have been developed with the objective of detecting ARs. The primary component of many AR detection schemes is a percentile thresholding of integrated water vapor transport (IVT) magnitude, a measure representing the amount of water vapor transported in an atmospheric column which varies over time and space. Motivated by the need for versatile estimation of a single quantile over time and space, we present an extended dynamic quantile linear model (exDQLM) by specifying the observational errors of a dynamical linear model to be distributed from an extended asymmetric Laplace (exAL). The exDQLM facilitates more flexibility than the standard Bayesian parametric quantile regression approach utilizing the asymmetric Laplace (AL), a special case of the exAL. Through a simulation study, we find the exDQLM more robust for non-standard distributions performing better in both quantile estimation and predictive accuracy. The construction of the exAL through a structured mixture of normal distributions enables Bayesian posterior simulation through a Markov chain Monte Carlo (MCMC) algorithm, however the latent parameters introduce computational challenges for model selection and large datasets. An efficient expectation maximization (EM) algorithm is proposed as a possible solution. The EM algorithm enables preliminary exploration of the IVT magnitude 0.85-quantile at one spatial location. Multivariate and spatial interaction between the IVT magnitudes motivate proposals for possible extension of the exDQLM to these settings.