Power properties if invariant tests for spatial autocorrelation in linear regression

This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is include

Y-Mars: An Astrobiological Analogue of Martian Mudstone

NASA's Mars Science Laboratory mission has collected evidence of a long‐lasting habitable environment in the Sheepbed sediments of Gale Crater on Mars. The geochemistry of this mudstone suggests that the lake filling the crater in Mars' past had a neutral pH and low salinity and contained elements and redox couples required by life. We produced a geochemical analogue to the Sheepbed mudstone by mixing a collection of its primary minerals to match the X‐Ray diffraction data from Mars Science Laboratory. Here we describe the production of the Y‐Mars (Yellowknife‐Mars) analogue and characterize its properties, including the presence of background carbon, nitrogen, and sulfur. We highlight some of the unavoidable issues involved in making analogues, especially for astrobiological applications. The Y‐Mars analogue has a number of applications for astrobiological research, but more analogues are required to properly represent the diversity of Martian sedimentary contexts