Comments on: Comparing and Selecting Spatial Predictors Using Local Criteria

We would like to congratulate the authors for producing this interesting and novel methodology for comparison of spatial fields. It is important that this problem be discussed and expanded, especially in the context of large data sets, which is undoubtedly one of the main challenges that any statistician working with environmental space-time data has to face in contemporary research. We have divided our comments in three sections that cover separate (albeit intertwined) topics. In Section 2, we link this work with previous literature on hypothesis testing with multiple predictors and discuss the consequences of not accounting for predictor uncertainty. In Section 3, we discuss the interpretability of Locally Selected Predictors (LSP) and Globally Selected Predictors (GSP) estimates and potential challenges around this issue, while in Section 4 we expand some points on oversmoothing and scalability for large data sets that have arisen in this work.