In this paper, we critically examine the prevalent practice of using additive mixtures of Mat\'ern kernels in single-output Gaussian process (GP) models and explore the properties of multiplicative mixtures of Mat\'ern kernels for multi-output GP models. For the single-output case, we derive a series of theoretical results showing that the smoothness of a mixture of Mat\'ern kernels is determined by the least smooth component and that a GP with such a kernel is effectively equivalent to the least smooth kernel component. Furthermore, we demonstrate that none of the mixing weights or parameters within individual kernel components are identifiable. We then turn our attention to multi-output GP models and analyze the identifiability of the covariance matrix $A$ in the multiplicative kernel $K(x,y) = AK_0(x,y)$, where $K_0$ is a standard single output kernel such as Mat\'ern. We show that $A$ is identifiable up to a multiplicative constant, suggesting that multiplicative mixtures are well suited for multi-output tasks. Our findings are supported by extensive simulations and real applications for both single- and multi-output settings. This work provides insight into kernel selection and interpretation for GP models, emphasizing the importance of choosing appropriate kernel structures for different tasks.

MOTIVATION: Deriving biological insights from genomic data commonly requires comparing attributes of selected genomic loci to a null set of loci. The selection of this null set is non-trivial, as it requires careful consideration of potential covariates, a problem that is exacerbated by the non-uniform distribution of genomic features including genes, enhancers, and transcription factor binding sites. Propensity score-based covariate matching methods allow the selection of null sets from a pool of possible items while controlling for multiple covariates; however, existing packages do not operate on genomic data classes and can be slow for large data sets making them difficult to integrate into genomic workflows. RESULTS: To address this, we developed matchRanges, a propensity score-based covariate matching method for the efficient and convenient generation of matched null ranges from a set of background ranges within the Bioconductor framework. AVAILABILITY AND IMPLEMENTATION: Package: https://bioconductor.org/packages/nullranges, Code: https://github.com/nullranges, Documentation: https://nullranges.github.io/nullranges.

MOTIVATION: Enrichment analysis is a widely utilized technique in genomic analysis that aims to determine if there is a statistically significant association between two sets of genomic features. To conduct this type of hypothesis testing, an appropriate null model is typically required. However, the null distribution that is commonly used can be overly simplistic and may result in inaccurate conclusions. RESULTS: bootRanges provides fast functions for generation of block bootstrapped genomic ranges representing the null hypothesis in enrichment analysis. As part of a modular workflow, bootRanges offers greater flexibility for computing various test statistics leveraging other Bioconductor packages. We show that shuffling or permutation schemes may result in overly narrow test statistic null distributions and over-estimation of statistical significance, while creating new range sets with a block bootstrap preserves local genomic correlation structure and generates more reliable null distributions. It can also be used in more complex analyses, such as accessing correlations between cis-regulatory elements (CREs) and genes across cell types or providing optimized thresholds, e.g. log fold change (logFC) from differential analysis. AVAILABILITY AND IMPLEMENTATION: bootRanges is freely available in the R/Bioconductor package nullranges hosted at https://bioconductor.org/packages/nullranges.

SUMMARY: Exclusion regions are sections of reference genomes with abnormal pileups of short sequencing reads. Removing reads overlapping them improves biological signal, and these benefits are most pronounced in differential analysis settings. Several labs created exclusion region sets, available primarily through ENCODE and Github. However, the variety of exclusion sets creates uncertainty which sets to use. Furthermore, gap regions (e.g. centromeres, telomeres, short arms) create additional considerations in generating exclusion sets. We generated exclusion sets for the latest human T2T-CHM13 and mouse GRCm39 genomes and systematically assembled and annotated these and other sets in the excluderanges R/Bioconductor data package, also accessible via the BEDbase.org API. The package provides unified access to 82 GenomicRanges objects covering six organisms, multiple genome assemblies, and types of exclusion regions. For human hg38 genome assembly, we recommend hg38.Kundaje.GRCh38_unified_blacklist as the most well-curated and annotated, and sets generated by the Blacklist tool for other organisms. AVAILABILITY AND IMPLEMENTATION: https://bioconductor.org/packages/excluderanges/. Package website: https://dozmorovlab.github.io/excluderanges/.

MOTIVATION: Allelic expression analysis aids in detection of cis-regulatory mechanisms of genetic variation, which produce allelic imbalance (AI) in heterozygotes. Measuring AI in bulk data lacking time or spatial resolution has the limitation that cell-type-specific (CTS), spatial- or time-dependent AI signals may be dampened or not detected. RESULTS: We introduce a statistical method airpart for identifying differential CTS AI from single-cell RNA-sequencing data, or dynamics AI from other spatially or time-resolved datasets. airpart outputs discrete partitions of data, pointing to groups of genes and cells under common mechanisms of cis-genetic regulation. In order to account for low counts in single-cell data, our method uses a Generalized Fused Lasso with Binomial likelihood for partitioning groups of cells by AI signal, and a hierarchical Bayesian model for AI statistical inference. In simulation, airpart accurately detected partitions of cell types by their AI and had lower Root Mean Square Error (RMSE) of allelic ratio estimates than existing methods. In real data, airpart identified differential allelic imbalance patterns across cell states and could be used to define trends of AI signal over spatial or time axes. AVAILABILITY AND IMPLEMENTATION: The airpart package is available as an R/Bioconductor package at https://bioconductor.org/packages/airpart. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.