Statistical Methods for Evaluating the Environmental Sustainability

This paper represents a preliminary attempt at exploring a series of statistical methods for evaluating the environmental sustainability of urban and rural territories. We briefly present and discuss modern statistical techniques to study the relationships between a set of air pollutants. In particular, we focus on multivariate methods to explore air quality data after encoding the atmospheric measurements as covariance matrices that summarise the relationships among pollutants at different monitoring sites. In fact, a key property of covariance matrices is that they lie on a Riemannian manifold, and we exploit this fact to facilitate the exploratory analyses. Future directions of our work include extending the methods discussed here in a geostatistical setting, employing techniques such as Kriging for Riemannian data.