Spatial transcriptomic studies are becoming increasingly common and large, posing important statistical and computational challenges for many analytic tasks. Here, we present SPARK-X, a non-parametric method for rapid and effective detection of spatially expressed genes in large spatial transcriptomic studies. SPARK-X not only produces effective type I error control and high power but also brings orders of magnitude computational savings. We apply SPARK-X to analyze three large datasets, one of which is only analyzable by SPARK-X. In these data, SPARK-X identifies many spatially expressed genes including those that are spatially expressed within the same cell type, revealing new biological insights.

Tumors are complex tissues of cancerous cells surrounded by a heterogeneous cellular microenvironment with which they interact. Single-cell sequencing enables molecular characterization of single cells within the tumor. However, cell annotation—the assignment of cell type or cell state to each sequenced cell—is a challenge, especially identifying tumor cells within single-cell or spatial sequencing experiments. Here, we propose ikarus, a machine learning pipeline aimed at distinguishing tumor cells from normal cells at the single-cell level. We test ikarus on multiple single-cell datasets, showing that it achieves high sensitivity and specificity in multiple experimental contexts. **InferCNV** is a Bayesian method, which agglomerates the expression signal of genomically adjointed genes to ascertain whether there is a gain or loss of a certain larger genomic segment. We have used **inferCNV** to call copy number variations in all samples used in the manuscript.

Many spatially resolved transcriptomic technologies do not have single-cell resolution but measure the average gene expression for each spot from a mixture of cells of potentially heterogeneous cell types. Here, we introduce a deconvolution method, conditional autoregressive-based deconvolution (CARD), that combines cell-type-specific expression information from single-cell RNA sequencing (scRNA-seq) with correlation in cell-type composition across tissue locations. Modeling spatial correlation allows us to borrow the cell-type composition information across locations, improving accuracy of deconvolution even with a mismatched scRNA-seq reference. **CARD** can also impute cell-type compositions and gene expression levels at unmeasured tissue locations to enable the construction of a refined spatial tissue map with a resolution arbitrarily higher than that measured in the original study and can perform deconvolution without an scRNA-seq reference. Applications to four datasets, including a pancreatic cancer dataset, identified multiple cell types and molecular markers with distinct spatial localization that define the progression, heterogeneity and compartmentalization of pancreatic cancer.