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Identifying genes that display spatial expression patterns in spatially resolved transcriptomic studies is an important first step toward characterizing the spatial transcriptomic landscape of complex tissues. Here we present a statistical method, SPARK, for identifying spatial expression patterns of genes in data generated from various spatially resolved transcriptomic techniques. SPARK directly models spatial count data through generalized linear spatial models. It relies on recently developed statistical formulas for hypothesis testing, providing effective control of type I errors and yielding high statistical power. With a computationally efficient algorithm, which is based on penalized quasi-likelihood, SPARK is also scalable to datasets with tens of thousands of genes measured on tens of thousands of samples. Analyzing four published spatially resolved transcriptomic datasets using SPARK, we show it can be up to ten …