MCMC-CE: A Novel and Efficient Algorithm for Estimating Small Right-Tail Probabilities of Quadratic Forms with Applications in Genomics

Ong, V. Q.; Choi, B. N.; Lundy, D. P.; Xu, H.; Ghosh, S.; Jiang, H.; Shi, Y.

doi:10.1101/2025.03.16.643492

Home/Archive/bioRxiv

bioRxiv · 10.1101/2025.03.16.643492

MCMC-CE: A Novel and Efficient Algorithm for Estimating Small Right-Tail Probabilities of Quadratic Forms with Applications in Genomics

Ong, V. Q.·Choi, B. N.·Lundy, D. P.·Xu, H.·Ghosh, S.·Jiang, H.·Shi, Y.

View original source ↗Export metadata ↓

Abstract

Quadratic forms of multivariate normal variables play a critical role in statistical applications, particularly in genomics and bioinformatics. However, accurately computing small right-tail probabilities (p-values) for large-scale quadratic forms is computationally challenging due to the intractability of their probability distributions, as well as significant numerical constraints and computational burdens. To address these problems, we propose MCMC-CE, an innovative algorithm that integrates Markov Chain Monte Carlo (MCMC) sampling with the cross-entropy (CE) method, coupled with leading-eigenvalue extraction and Satterthwaite-type approximation techniques. Our approach efficiently estimates small p-values for quadratic forms with their ranks exceeding 10,000. Through extensive simulation studies and real-world applications in genomics, including genome-wide association studies and pathway enrichment analyses, our method demonstrates advantageous numerical accuracy and computational reliability compared to existing approaches such as Davies, Imhofs, Farebrothers, Liu-Tang-Zhangs and saddlepoint approximation methods. MCMC-CE provides a robust and scalable solution for accurately computing small p-values for quadratic forms, facilitating more precise statistical inference in large-scale genomic studies.

Source connections

Published article ↗

Explore related subjects

bioinformatics Preprint

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Ong, V. Q., Choi, B. N., Lundy, D. P., Xu, H., Ghosh, S., Jiang, H., Shi, Y.. 2025-03-17. MCMC-CE: A Novel and Efficient Algorithm for Estimating Small Right-Tail Probabilities of Quadratic Forms with Applications in Genomics. https://doi.org/10.1101/2025.03.16.643492

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related preprints

bioRxiv2026

spatialMET: an open and scalable framework for spatial metabolomics analysis

Mass spectrometry imaging (MSI) enables spatially resolved metabolomics in intact tissue sections, but analysis remains challenging at scale. Existing MSI workflows often require users to combine multiple software tools, while others rely on proprietary vendor software that limits interoperability and reproducibility. To address these challenges, we developed spatialMET, an open-source framework that provides an end-to-end workflow for MSI analysis. spatialMET provides a unified platform for preprocessing, spatial domain detection, and visualization. Downstream analyses include differential abundance testing, spatial autocorrelation and gradient analysis, dimensionality reduction, and correlation network analysis. Spatial domain detection uses hcdist, a C-based hierarchical clustering implementation that substantially reduces runtime and memory use relative to existing R-based approaches. spatialMET can be run through an interactive R Shiny application or as a standalone command-line workflow for larger datasets or high-performance computing environments. Applied to mouse small cell lung cancer MALDI-MSI data containing 284,673 pixels, spatialMET identified tumor-associated, stromal, and adjacent lung spatial domains that aligned with matched histology. Differential abundance analysis identified 117 m/z features that differed between tumor and stromal regions, while spatial autocorrelation analyses revealed spatially structured abundance patterns. Applying spatialMET to mouse lung adenocarcinoma data from an entire lung lobe containing 338,477 pixels further demonstrated scalability and captured spatial heterogeneity across tumor and surrounding lung tissue. In summary, spatialMET provides a scalable, open-source framework for end-to-end spatial metabolomics analysis, and it is distributed as a Docker container for reproducible deployment. Source code and installation instructions are available at https://github.com/biodatalab/spatialMET.

bioinformatics↗

bioRxiv2026

Probing the transcriptome response to shivering in skeletal muscle using a multilayered bioinformatics approach

Cold acclimation holds therapeutic potential for improving metabolic health. We previously demonstrated that repeated cold-induced shivering enhances insulin sensitivity in humans. However, the molecular pathways that underlie the skeletal muscle shivering response, and how these relate to beneficial physiological effects, remain poorly understood. In this study, we combined complementary bioinformatics approaches to allow in-depth analysis of the transcriptomic response of human skeletal muscle to repeated shivering. We identified a robust transcriptional signature and show a sex-specific component in the shivering skeletal muscle response, which seemed to diminish following cold adaptation. Our findings provide mechanistic insights into cold-induced muscle adaptations, shed light on potential interesting molecular targets for further investigation, and emphasize the importance of including both sexes in future cold acclimation studies.

bioinformatics↗

bioRxiv2026

An Information Geometry approach to model topological trajectories and Gene Expression Radius from UMAP geometry.

Understanding the relationship between gene expression dynamics and cellular identity remains a central challenge in single cell biology. Here, we introduce a novel computational and mathematical framework that integrates information geometry, fuzzy topology, and UMAP analysis to model gene expression landscapes derived from single cell RNA sequencing data. We formalize gene expression data as a fuzzy topological space, where interactions between expression points are governed by probabilistic distributions inspired by manifold learning approaches such as UMAP. Within this framework, we define an information geometric structure through a Fisher metric induced by these distributions, enabling the computation of geodesic trajectories that capture cellular differentiation processes. A key contribution of this work is the derivation of analytical conditions, expressed as expression radius formulas, that characterize local neighborhoods in gene expression space. These conditions allow for the identification of genes associated with stem cell states and predictions in transitional cell types in future work. Application of the proposed framework to single cell datasets reveals biologically meaningful gene sets enriched in key regulatory pathways and transcription factors, demonstrating the capacity of our approach to uncover latent structure in complex gene expression data. Our results suggest that integrating differential geometry with statistical learning theory offers a powerful paradigm for modeling genotype and phenotype relationships and cellular state transitions, with potential implications for precision medicine and systems biology.

bioinformatics↗