An Additive Spatiotemporal Covariance Function Using Stream and River Distance Open Access

Whelan, Denis (Fall 2017)

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BACKGROUND: Modeling all geo-referenced phenomenon using strictly Euclidean distance is restrictive and often implausible, especially when measuring the movement of organisms in infectious disease research and ecology. Studying the transmission of diarrheal disease incidence in developing countries involves studying the movement of waterborne pathogens. In order to effectively estimate the spread of diarrheal disease, spatiotemporal heterogeneity must be considered explicitly.

OBJECTIVE: This paper presents a covariance function that incorporates a weighted combination of multiple distance metrics to estimate spatiotemporal dependence of a Gaussian outcome using a Bayesian framework.

DATA: Twenty-one communities in northwestern Ecuador were randomly selected from data collected as a part of the ECODESS study (Ecología, Desarollo, Salud y Sociedad), which was geared towards achieving a better understanding of community-level risk factors of diarrheal disease by examining environmental and ecological factors.

METHODS: An additive covariance function incorporating both Euclidean and river distance is proposed to estimate spatiotemporal dependence. Metropolis-Hastings and Gibbs sampling are used for MCMC parameter estimation. We use three fit measures designed for Bayesian models to compare the model fit of the additive covariance function to a model with Euclidean distance only and a model with river distance only.

RESULTS: The additive covariance function incorporating both Euclidean and river distance was the best performing model in terms of all three Bayesian model fit criteria only when the simulated Gaussian was generated using a combination of those simulated distance matrices. Results were mixed when this method was applied to observed data.

CONCLUSIONS: This paper lays the foundation for estimation of covariance functions using multiple distance matrices with wide applications in infectious disease and ecology research and can motivate a range important methodological extensions.

Table of Contents

Introduction: pages 1-3

Data: page 4

Methods: pages 5-11

Simulation: pages 12-13

Analysis: pages 14-15

Discussion: pages 16-18

Tables & Figures: pages 19-37

Appendix: pages 38-45

Works Cited: pages 46-48

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