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Abstract:
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A spatial stream network (SSN) model is a geostatistical model with the spatial dependencies defined through a kernel convolution to incorporate the characteristics of a stream network. These characteristics include the use of stream distance, rather than Euclidean distance, and that flow direction and volume may affect the strength and direction of autocorrelation. SSN models are currently fit using maximum likelihood or restricted maximum likelihood in R. We propose a Bayesian version of the model. The Bayesian framework adds flexibility to the model structure, such as the ability to add an offset to a Poisson model. The Bayesian approach also does not rely on an approximation algorithm, resulting in more reliable estimates of the spatial parameters for the generalized linear models. Results from simulations demonstrate its equivalence to maximum likelihood estimates for Gaussian data, and more accurate estimates of the spatial parameters and smaller variances for fixed effects coefficients for Poisson data. We exemplify the Bayesian version's flexibility and comparable performance with a data set of fish counts in the South Platte River basin in northeastern Colorado.
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