Date of Completion

8-3-2020

Embargo Period

8-3-2020

Keywords

Long Island sound, wave heights, MCMC, INLA, logistic regression, GLM, DGLM, quantile reqression, expectile regression, hqreg, SALES

Major Advisor

Nalini Ravishanker

Associate Advisor

Haim Bar

Associate Advisor

James O'Donnell

Field of Study

Statistics

Open Access

Open Access

Abstract

Current marine science methods for modeling wave data typically assume that wave height distributions belong to limited class within the exponential family. Alternatively, models emphasize physics principles over statistical methods. In this dissertation, we investigate the predictive power of wave height histories as well as exogenous predictors. We develop binary time series models for wave height over a threshold in both frequentist and Bayesian frameworks. Within the Bayesian framework, we fit Dynamic Generalized Linear Models (DGLM) using Integrated Nested Laplace Approximations and demonstrate advantages over classical methods. We further investigate the quantiles and expectiles of the continuous- valued wave height time series. Models with high lag orders are and hundreds of predictors are considered. Using regularized quantile and expectile regression with the Elastic Net penalty, we fit sparse models to characterize the upper tail of the wave height distribution and offer predictions of high quantiles and expectiles as a function of local sea state.

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