Spatial transcriptomics preserves tissue organization while measuring gene expression, but measurements are sensitive to technical variability such as library size differences, slide-level effects, and spatial artifacts. Most normalization approaches treat normalization as a separate preprocessing step and then perform downstream analyses on normalized values as fixed inputs, thereby ignoring uncertainty introduced during normalization. To address these issues, the authors introduce GPSNorm (Gaussian Process Spatial Normalization), a Bayesian framework that jointly models technical variation, spatial structure, and biological signal in a unified hierarchical model.
The stated intent of GPSNorm is to improve robustness and interpretability of downstream inference by accounting for uncertainty from the normalization step and by explicitly modeling spatial technical effects instead of removing them through ad hoc preprocessing.
GPSNorm represents observed gene expression counts using a negative binomial latent Gaussian model. The spatial component of the model is formulated as a Gaussian Markov random field (GMRF) that approximates a Gaussian process, enabling spatial smoothing and explicit modeling of spatially structured technical effects. By placing the spatial component inside a hierarchical Bayesian model together with gene- and slide-level effects, GPSNorm jointly captures biological signal and multiple layers of technical variation.
Modeling counts with a negative binomial latent Gaussian framework allows the approach to account for overdispersion common in spatial transcriptomics count data, while the GMRF representation provides a computationally tractable approximation to a full Gaussian process.
GPSNorm performs efficient approximate Bayesian inference using the Integrated Nested Laplace Approximation (INLA). INLA produces posterior distributions for model parameters and latent quantities, which the authors highlight as a mechanism to propagate normalization uncertainty into downstream analyses such as differential expression and log-fold change estimation.
By returning posterior estimates rather than single-point normalized values, GPSNorm enables downstream inference to account for the uncertainty introduced by normalization and spatial modeling, aligning preprocessing and inference within a single probabilistic framework.
The authors evaluated GPSNorm in simulations that were anchored to empirical spatial transcriptomics data. According to the report, GPSNorm accurately recovered spatial technical structure in these simulations and improved log-fold change estimation relative to existing normalization methods. The article states these comparative improvements but does not include full numerical details in the abstract; readers should consult the full preprint for complete simulation design, metrics, and quantitative comparisons.
GPSNorm was applied to three real-world spatial transcriptomics datasets to assess practical performance and biological interpretability:
In these applications the authors report that GPSNorm demonstrated improved preservation of biologically expected spatial patterns and marker gene contrasts compared with other normalization approaches, indicating that joint modeling of technical and spatial effects can enhance the recovery of biologically meaningful signals in spatial datasets.
An open-source R implementation of GPSNorm is available at https://github.com/Tiny-Quant/GPSNorm. The preprint provides the code link and notes that data and code resources are associated with the manuscript. Because this work is presented as a preprint, users should review the repository and preprint for implementation details, usage instructions, and any example analyses shared by the authors.
This manuscript is a bioRxiv preprint and has not been peer reviewed; the authors explicitly note this status. The abstract and manuscript declare no competing interests. Funding sources listed include several National Institutes of Health grants and support from the Cancer Prevention and Research Institute of Texas. For detailed limitations, validation, and benchmark statistics, readers should consult the full preprint and associated supplementary materials.
Overall, GPSNorm proposes a principled Bayesian approach that combines a negative binomial count model, a GMRF-based spatial component approximating a Gaussian process, and INLA-based inference to jointly normalize spatial transcriptomics data while propagating uncertainty into downstream analyses. The authors report simulation and empirical evidence of improved recovery of spatial technical structure and biologically relevant patterns, and they provide an R implementation for reproducibility.