Statistics and Its Interface

Volume 16 (2023)

Number 3

Two-stage multivariate dynamic linear models to extract environmental and climate signals in coastal ecosystem data

Pages: 419 – 431



Jacob Strock (University of Rhode Island, Narragansett, R.I., U.S.A.)

Gavino Puggioni (University of Rhode Island, Narragansett, R.I., U.S.A.)

Susanne Menden-Deuer (University of Rhode Island, Narragansett, R.I., U.S.A.)


In environmental time series the presence of missing data, desire for multiple modeling structures, non-simultaneous data streams and computationally costly inference in highly parameterized model structures bring major challenges. In this work, we describe how multistage dynamic linear model (DLM) structures can be used to concomitantly describe long-term patterns, infer missing data, test predictive relationships, and altogether facilitate model development where multiple objectives and data streams may exist. We demonstrate the utility of this modeling approach with long-term data from Narragansett Bay (NB), Rhode Island, USA which has undergone major ecological changes including reductions in anthropogenic nutrient pollution. In a first stage, DLMs were used both to interpolate missing data and describe changes in both seasonality and long-term trend for nitrogenous nutrients and size structure of phytoplankton communities. These models revealed a long-term decline in large phytoplankton, and intensifying seasonal blooms for smaller phytoplankton. In a second modeling stage, parameters with associated uncertainty from stage 1 were used as covariates to test how features of the nitrogen series impacted phytoplankton. Conditional on the posterior inference of predictors modeled in stage 1, the dynamic regression revealed a newly discovered seasonal dependence of large phytoplankton on nitrogen sources.


time series, dynamic linear model, pollution, oceanography

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This material is based upon work supported in part by the National Science Foundation (EPSCoR Cooperative Agreement OIA-1655221, Biological Oceanography OCE-1736635). Jacob P. Strock was supported by the National Space Grant College and Fellowship Program, Space Grant Opportunities (NASA STEM -NNX15AI06H).

Received 1 March 2021

Accepted 12 March 2022

Published 14 April 2023