Abstract

Since the 1999 publication of Spatial Interpolation: Some Theory for Kriging, there have been broad advances on many fronts in spatial statistics. Areas that have seen particular progress include the development of non-stationary spatial process models, computational methods and the emergence of space-time statistics as a distinct and vibrant field of statistics. At the same time, a number of fundamental theoretical problems raised in my book remain unsolved. Other areas in need of greater attention include the development of a broader array of models for anisotropy, approaches for handling environmental data displaying stochastic volatility and methods for studying extreme environmental events over large spatial scales. Perhaps the biggest challenge in spatial statistics is keeping up with the rapidly increasing size of environmental datasets, especially those obtained via remote sensing. While we can expect lots of progress in spatial statistics over the coming decades, it is always important to step back and consider whether we are asking the right questions, which requires a deep engagement with both theory and applications.