Covariate-Driven Non-Stationary Models in Stan with Application to Water Quality in North American Lakes

• Activity Number: 190 - Contributed Poster Presentations: Section on Statistics and the Environment
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Pavel Chernyavskiy* and Marie-Agnes Tellier and Sarah M Collins
• Companies: University of Wyoming and University of Wyoming and University of Wyoming
• Keywords: non-stationary; spatial; Bayesian; Stan; lakes

Abstract

Freshwater ecosystems are vulnerable to anthropogenic changes that occur at disparate spatial scales, leading to nutrient pollution and poor water quality. Recent non-stationary models that admit covariates into the mean, variance, and covariance functions can improve our understanding of the mechanisms by which environmental stressors impact freshwater resources. Our project has three goals: 1) implement covariate-driven non-stationary models via Hamiltonian Monte Carlo (HMC); 2) compare alternative parameterizations and prior specifications via a simulation study; and 3) investigate correlates of non-stationary spatial dependence for water quality in North America. Here, we analyze water clarity (“secchi”) within Indiana and Ohio (N=403). We estimated non-stationary models introduced by Risser and Calder (2015) using HMC in Stan, which does not require conjugate priors and produces more effective samples/iteration than Gibbs samplers. Precipitation, agriculture, and lake depth explained broad-scale variation in the mean. We found evidence of anisotropy and a non-stationary spatial variance: spatial SD increased by a factor of 1.39 per SD increase of agriculture in the watershed.