Date of Award

2021

Degree Type

Thesis

Degree Name

Master of Science in Statistics

Department

Computer Science and Statistics

First Advisor

Gavino Puggioni

Abstract

Within the past 50 years, Narragansett Bay has undergone major physical and chemical changes including climate-induced warming and policy-driven reductions in anthropogenic nutrient pollution. These long-term changes have the capacity to transform the ecological function of Narragansett Bay, but may also represent a case study for global oceanic changes. Despite its importance, the long-term response of ecosystems to climatological change remains uncertain, as well as the consistency of biological interactions with the environment over time. I explore these uncertainties here using Bayesian dynamic linear models (DLMs) to investigate the Narragansett Bay Long-Term Plankton Time Series. In a first stage, DLMs were used both to interpolate missing data and describe changes in seasonality and long-term trend for nitrogenous nutrients, water temperature, and size structure of phytoplankton communities. Among complex physical and chemical changes observed, these models revealed a long-term decline in large phytoplankton and intensifying seasonal blooms for smaller phytoplankton. These changes in size structure of biological communities were expanded through analysis of cross correlations and a second modeling stage where the imputed nitrogen series was used as a predictor of phytoplankton levels in a multivariate dynamic linear regression model (DLR). The DLR revealed a newly discovered seasonal dependence of large phytoplankton on nitrogen sources. Results suggested highly dynamic states and the need for discount specification of covariance matrices. This motivated more general analysis of model selection in time series with high stochasticity and long intervals of missing data. Through simulated data and metrics of model fit including information criteria and forecasting errors, I explored model selection as well as standard and practical discounting methods in series with long intervals of missingness. These analyses highlight one-step-ahead root mean square forecast error as a relatively consistent selection tool, but also evidence the uncertainty in accurate recovery of discount factors in general, and potential impacts on model inference.

Available for download on Friday, April 01, 2022

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