The problem. Once you have spatial transcriptomics data, the first analytical question is: which genes show spatial structure — expression that varies with position in a non-random way — versus genes that are just noisily scattered? Ordinary differential expression asks about conditions, not coordinates; you need a test built around location itself.

The idea. SpatialDE models expression as a function of spatial coordinates using Gaussian processes: it decomposes each gene’s variance into a spatial component (explained by a covariance function over positions) and a residual, then tests whether the spatial component is significant. Genes whose expression covaries with location — beyond what noise would produce — are flagged as spatially variable, with a characteristic length scale.

Why it matters. This is the foundational statistical primitive for spatial data — the “which genes matter, spatially” step that precedes domain-finding and interpretation. It’s a direct conceptual translation of a tool I know (differential expression) into the spatial setting, using the Gaussian-process machinery. For any spatial analysis, including the STU’s, identifying spatially variable genes is an early, essential move, and this defined how to do it rigorously.

Verdict. Foundational for spatial statistics; later methods (SPARK, and domain-aware approaches) refine the model and scale it. Read it as the spatial counterpart to differential expression — the test that turns coordinates into a question about genes.