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Abstract We propose a non‐stationary spatial model based on a normal‐inverse‐Wishart framework, conditioning on a set of nearest‐neighbors. The model, called nearest‐neighbor Gaussian process with random covariance matrices is developed for both univariate and multivariate spatial settings and allows for fully flexible covariance structures that impose no stationarity or isotropic restrictions. In addition, the model can handle duplicate observations and missing data. We consider an approach based on integrating out the spatial random effects that allows fast inference for the model parameters. We also consider a full hierarchical approach that leverages the sparse structures induced by the model to perform fast Monte Carlo computations. Strong computational efficiency is achieved by leveraging the adaptive localized structure of the model that allows for a high level of parallelization. We illustrate the performance of the model with univariate and bivariate simulations, as well as with observations from two stationary satellites consisting of albedo measurements. 

Greenspace positively impacts mental health. Previous research has focused on the greenspace-mental health relationship in urban areas. Yet, little work has looked at rural areas despite rural communities reporting similar rates of poor mental health outcomes and higher rates of suicide mortality compared with urban areas. This ecological research study examined the following research questions: (1) Do public and/or private greenspaces affect the spatial distribution of mental health outcomes in North Carolina? (2) Does this relationship change with rurality? Emergency department data for 6 mental health conditions and suicide mortality data from 2009 to 2018 were included in this analysis. Spatial error and ordinary least squares regressions were used to examine the influence of public and private greenspace quantity on mental health in rural and urban communities. Results suggest greenspace benefits mental health in rural and urban communities. The strength of this relationship varies with urbanity and between public and private greenspaces, suggesting a more complex causal relationship. Given the high case counts and often lower density of mental health care facilities in rural areas, focusing attention on low-cost mental health interventions, such as greenspace, is important when considering rural mental health care.