Extended Data Fig. 4: Batch effect characterization and evaluation of ground truth retrieval by uMAIA normalization.

a. MSI images for m/z 517.17 at different mediolateral positions (left) and corresponding background/foreground assignments (center) and histograms of intensity values (right), histogram bars colored by assignment (for example, foreground/background). b. Histogram displaying distribution of bootstrap estimates of first eigenvalue of empirical batch-effect matrix. c. Line plot showing fraction of explained variance contributed by each principal component of batch effects estimator. d. Hierarchical Bayesian model in plate notation, including metaparameters, latent variables, and data for intensity-distorted signal estimation. e. Generative model representation of model in (d). f. Fraction of explained variance contributed by each component from SVD as in (c) (black line) overlaid with those from simulation data (red line). g. Visualization of ellipsoid simulation. h. Intensity distributions in simulated data, comparing ground truth, simulated raw and uMAIA normalized data for 4 sections (left) with corresponding images shown (right). i. Box and whiskers plots quantifying similarity of corrected images with ground truth results are computed across 4 sections and variables of simulation. Similarity calculated with Spearman’s R between intensities. j. Scatterplots for ground truth, simulated raw, z-normalized, ComBat- and uMAIA-corrected data, each displaying mean molecule signal across sections. Low- (black), mid- (blue) and high-intensity (red) modes are highlighted. Variance for the three categories indicated by colored numbers. k. Schematic ABA ISH data simulation and evaluation. l. Visualization of images corresponding to gene Lct of ground truth (right) and simulated raw and corrected data with z-normalization, ComBat, and uMAIA (left). m. Root Mean Square Error (RMSE) distribution with respect to ground truth images for simulated raw data and data corrected with z-normalization, ComBat, and uMAIA. Lines drawn between genes and colored by relative increase or decrease of RMSE compared to simulated raw data. n. Fraction of explained variance contributed by each component from SVD applied to batch effect estimates for ISH simulations (black line) overlaid with those from shuffled data (red line). o. Heatmaps quantifying total number of false-positives and false-negatives after differential expression tests across all genes for 5 major anatomical regions for simulated data and data corrected with different methods. p. False-positive and false-negative rates after differential expression tests using bootstrapped sections (n=20). Boxplots indicate interquartile range and median. Distributions shown for ground truth (gt), simulated raw and corrected data with z-normalization, ComBat and uMAIA.