Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Bayesian computational modeling”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2Linked to original sources
PubMed2025

Bayesian classification of OXPHOS deficient skeletal myofibres.

Mitochondria are organelles in most human cells which release the energy required for cells to function. Oxidative phosphorylation (OXPHOS) is a key biochemical process within mitochondria required for energy production and requires a range of proteins and protein complexes. Mitochondria contain multiple copies of their own genome (mtDNA), which codes for some of the proteins and ribonucleic acids required for mitochondrial function and assembly. Pathology arises from genetic defects in mtDNA and can reduce cellular abundance of OXPHOS proteins, affecting mitochondrial function. Due to the continuous turn-over of mtDNA, pathology is random and neighbouring cells can possess different OXPHOS protein abundance. Estimating the proportion of cells where OXPHOS protein abundance is too low to maintain normal function is critical to understanding disease severity and predicting disease progression. Currently, one method to classify single cells as being OXPHOS deficient is prevalent in the literature. The method compares a patient's OXPHOS protein abundance to that of a small number of healthy control subjects. If the patient's cell displays an abundance which differs from the abundance of the controls then it is deemed deficient. However, due to the natural variation between subjects and the low number of control subjects typically available, this method is inflexible and often results in a large proportion of patient cells being misclassified. These misclassifications have significant consequences for the clinical interpretation of these data. We propose a single-cell classification method using a Bayesian hierarchical mixture model, which allows for inter-subject OXPHOS protein abundance variation. The model accurately classifies an example dataset of OXPHOS protein abundances in skeletal muscle fibres (myofibres). When comparing the proposed and existing model classifications to manual classifications performed by experts, the proposed model results in estimates of the proportion of deficient myofibres that are consistent with expert manual classifications.

Oxidative Phosphorylation↗
PubMed2026

TPMM: three-component posterior mixture model enables robust inverton detection in low-depth metagenomes and suggests potential viral invertons.

SUMMARY: Bacterial phase variation enables reversible, locus-specific phenotypic switching, often driven by DNA inversion (invertons). To identify these events, researchers commonly rely on sequencing reads that provide orientation-specific support. Metagenomic sequencing, which captures total genetic material independent of cultivation, offers a powerful platform for the comprehensive study of invertons. However, computational inverton calling from metagenomic data is difficult at low sequencing depth: hard read-support cutoffs can miss true events, while sequence-only predictors lack read-backed interpretability and uncertainty quantification. To address this, we present TPMM, a three-component posterior mixture model for inverton calling in metagenomic data. TPMM explicitly incorporates sequencing depth to formulate inverton detection as a probabilistic mixture problem. Starting from candidates flanked by inverted repeats, the model classifies the candidates into noise, low-probability, or high-probability inversion signals using read evidence. Finally, TPMM assigns posterior probabilities as soft labels and applies cumulative Bayesian False Discovery Rate control to robustly identify true invertons. On two real gut metagenomic datasets, TPMM agrees well with PhaseFinder at high depth but recovers substantially more invertons under systematic downsampling, demonstrating superior performance in sparse-data regimes. We further examine potential reversible inversion elements in viral genomes and provide supporting analyses, suggesting a broader scope for inversion-mediated regulation. AVAILABILITY: The source code of TPMM is available via: https://github.com/KennyxxD/TPMM.

Metagenomics↗
PubMed1978

General problems in medical decision making with comments on ROC analysis.

Medical decision-making studies continue to focus on two questions: How do physicians make decisions? How should physicians make decisions? Researchers pursuing the first question emphasize human cognitive processes and the programming of symbol systems to model observed human behavior. Those researchers concentrating on the second question assume that there is a standard of performance against which the physician's decisions can be judged, and to help the physician improve his performance, an array of tools is proposed. These tools include decision trees, Bayesian analysis, decision matrices, receiver operating characteristics (ROC) analysis, and cost-benefit considerations including utility measures. Medical decision-making questions must be answered in an ethical context where ethics and decision analysis are interviewed.

Bayes Theorem↗
PubMed2025

BISON: bi-clustering of spatial omics data with feature selection.

MOTIVATION: The advent of next-generation sequencing-based spatially resolved transcriptomics (SRT) techniques has reshaped genomic studies by enabling high-throughput gene expression profiling while preserving spatial and morphological context. Understanding gene functions and interactions in different spatial domains is crucial, as it can enhance our comprehension of biological mechanisms, such as cancer-immune interactions and cell differentiation in various regions. It is necessary to cluster tissue regions into distinct spatial domains and identify discriminating genes (DGs) that elucidate the clustering result, referred to as spatial domain-specific DGs. Existing methods for identifying these genes typically rely on a two-stage approach, which can lead to the phenomenon known as double-dipping. RESULTS: To address the challenge, we propose a unified Bayesian latent block model that simultaneously detects a list of DGs contributing to spatial domain identification while clustering these DGs and spatial locations. The efficacy of our proposed method is validated through a series of simulation experiments, and its capability to identify DGs is demonstrated through applications to benchmark SRT datasets. AVAILABILITY AND IMPLEMENTATION: The R/C++ implementation of BISON is available at https://github.com/new-zbc/BISON.

Software↗
PubMedDate not supplied

Evaluation of a computerized Bayesian model for diagnosis of renal cyst vs. tumor vs. normal variant from urogram information.

The diagnostic problem of cyst/tumor/normal variant raised on an excretory urogram leads to a decision to do needle aspiration or renal arteriography. This decision depends critically upon the probability distribution for the three diagnoses. A computerized Bayesian model of a uroradiologist's diagnostic process in solving the problem was developed. The model was based on subjective probabilities supplied by an experienced uroradiologist. The model was evaluated in terms of its ability to decrease the cost of further diagnosis regarding aspiration versus arteriography. The model's output was compared with decisions made by unaided radiologists viewing the same panel of 50 urogram test cases. Results indicate that the model does not improve upon the decisions made by a radiologist highly experienced with this diagnostic problem. However, the decisions made by unaided, less experienced radiologists result in greater cost than those of the model.

Angiography↗
PubMed2026

GAMMA: gap-aware motif mining under incomplete labeling with applications to MHC motifs.

MOTIVATION: Sequence motif identification is crucial for understanding molecular recognition, particularly in immune responses involving peptide binding to major histocompatibility complex (MHC) Class I molecules for antigen presentation to T cells. Traditionally, MHC Class I binding motifs are assumed to be contiguous and span nine amino acids. However, structural evidence suggests that binding may involve nonadjacent residues, challenging the assumptions of existing methods. RESULTS: In this study, we propose Gap-Aware Motif Mining Algorithm (GAMMA), a probabilistic framework designed to identify noncontiguous motifs under conditions of incomplete labeling. GAMMA employs Bayesian inference with Markov chain Monte Carlo sampling to jointly estimate motif parameters, binding locations, and the relative spacing between binding positions. Through extensive simulations and real-world applications to MHC Class I peptide datasets, GAMMA outperforms existing motif discovery tools such as GLAM2 in accurately localizing binding residues and identifying the underlying motifs. Notably, our results suggest that the true number of binding residues may be eight, fewer than the commonly assumed nine. In addition, for longer peptides, the model captures increased flexibility in the central region, consistent with structural observations that peptides may bulge in the middle. AVAILABILITY AND IMPLEMENTATION: The raw data and the source codes are available on GitHub (https://github.com/RanLIUaca/GAMMAmotif).

Amino Acid Motifs↗
PubMed2025

MRDtarget: A heuristic Gaussian approach for optimizing targeted capture regions to enhance Minimal Residual Disease detection.

Molecular residual disease (MRD) detection, initially developed for hematologic malignancies, has become a critical biomarker for monitoring solid tumors. MRD detection primarily relies on circulating tumor DNA (ctDNA) analysis using next-generation sequencing, offering high sensitivity and broad genomic coverage. However, challenges remain in designing cost-effective panels that maximize mutation detection while maintaining biological relevance. Fixed panels often lack sufficient patient-specific mutation coverage, while WES-based personalized MRD assays, despite their high sensitivity, are costly and less accessible. We developed a tumor comprehensive genomic profiling (CGP)-informed personalized MRD assay to detect tumor-derived mutations, which allowed us to design patient-specific personalized panels and meanwhile, provide a cost-effective alternative to whole exome sequencing (WES). To address these limitations, we developed MRDtarget, a heuristic multivariate Gaussian model-based targeted capture region selection method. By expanding beyond traditional hotspot regions, MRDtarget optimizes variant tracking for MRD detection, significantly improving sensitivity. Using a Bayesian inference-based heuristic approach, MRDtarget integrates multi-feature informativeness rates to identify optimal genomic regions for capture. Experimental results demonstrate that MRDtarget enables the detection of more variants per patient. This study underscores the importance of rational panel design to improve MRD sensitivity and provides a novel approach to enhance precision diagnostics and treatment for solid tumor patients.

Humans↗
PubMed2024

Evolution of homologous recombination rates across bacteria.

Bacteria are nonsexual organisms but are capable of exchanging DNA at diverse degrees through homologous recombination. Intriguingly, the rates of recombination vary immensely across lineages where some species have been described as purely clonal and others as "quasi-sexual." However, estimating recombination rates has proven a difficult endeavor and estimates often vary substantially across studies. It is unclear whether these variations reflect natural variations across populations or are due to differences in methodologies. Consequently, the impact of recombination on bacterial evolution has not been extensively evaluated and the evolution of recombination rate-as a trait-remains to be accurately described. Here, we developed an approach based on Approximate Bayesian Computation that integrates multiple signals of recombination to estimate recombination rates. We inferred the rate of recombination of 162 bacterial species and one archaeon and tested the robustness of our approach. Our results confirm that recombination rates vary drastically across bacteria; however, we found that recombination rate-as a trait-is conserved in several lineages but evolves rapidly in others. Although some traits are thought to be associated with recombination rate (e.g., GC-content), we found no clear association between genomic or phenotypic traits and recombination rate. Overall, our results provide an overview of recombination rate, its evolution, and its impact on bacterial evolution.

Bacteria↗
PubMed2026

BaGGLS: a Bayesian shrinkage framework for interpretable modeling of interactions in high-dimensional biological data.

MOTIVATION: Biological data is often high dimensional, noisy, and governed by complex interactions among sparse signals. This poses major challenges for interpretability and reliable feature selection. Tasks such as identifying motif interactions in genomics exemplify these difficulties, as only a small subset of biologically relevant features (e.g. motifs) are typically active, and their effects are often non-linear and context-dependent. While statistical approaches often result in more interpretable models, deep learning models have proven effective in modeling complex interactions and prediction accuracy, yet their black-box nature limits interpretability. RESULTS: We introduce BaGGLS, a flexible and interpretable probabilistic binary regression model designed for high-dimensional biological inference involving feature interactions. BaGGLS incorporates a Bayesian group global-local shrinkage prior, aligned with the group structure introduced by interaction terms. This prior encourages sparsity while retaining interpretability, helping to isolate meaningful signals and suppress noise. To enable scalable inference, we employ a partially factorized variational approximation that captures posterior skewness and supports efficient learning even in large feature spaces. In extensive simulations, we compare BaGGLS to frequentist probit regressions (unconstrained and with L1-penalty) as well as a probit model with Markov Chain Monte Carlo (MCMC) sampling under a horseshoe prior. We can show that BaGGLS outperforms the other methods with regard to interaction detection and is many times faster than MCMC sampling under the horseshoe prior. We also demonstrate the usefulness of BaGGLS in the context of interaction discovery from motif scanner outputs (e.g. Find Individual Motif Occurrences (FIMO)) and noisy attribution scores from deep learning models. This shows that BaGGLS is a promising approach for uncovering biologically relevant interaction patterns, with potential applicability across a range of high-dimensional tasks in computational biology. AVAILABILITY: Code is available at gitlab.com/dacs-hpi/baggls.

Bayes Theorem↗
PubMed2025

Core passive and facultative mTOR-mediated mechanisms coordinate mammalian protein synthesis and decay.

The maintenance of cellular homeostasis requires tight regulation of proteome concentration and composition. To achieve this, protein production and elimination must be robustly coordinated. However, the mechanistic basis of this coordination remains unclear. Here, we address this question using quantitative live-cell imaging, computational modeling, transcriptomics, and proteomics approaches. We found that protein decay rates systematically adapt to global alterations of protein synthesis rates. This adaptation is driven by a core passive mechanism supplemented by facultative changes in mechanistic/mammalian target of rapamycin (mTOR) signaling. Passive adaptation hinges on changes in the production rate of the machinery governing protein decay and allows for partial maintenance of the cellular proteome. Sustained changes in mTOR signaling provide an additional layer of adaptation unique to naive pluripotent stem cells, allowing for near-perfect maintenance of proteome composition. Our work unravels the mechanisms protecting the integrity of mammalian proteomes upon variations in protein synthesis rates. A record of this paper's transparent peer review process is included in the supplemental information.

TOR Serine-Threonine Kinases↗
PubMed2026

EscaPRRS-ORF5: a structure-aware evolutionary framework for prioritizing immune escape-prone variants in porcine reproductive and respiratory syndrome virus.

MOTIVATION: Porcine Reproductive and Respiratory Syndrome Virus (PRRSV) is a rapidly evolving RNA virus causing significant economic losses, posing a formidable challenge to vaccine efficacy due to its high mutational variability and immune escape. As the viral mutants evolve, their ability to sustain in population is driven by a range of host biology factors such as receptor binding, fusion, and uncoating. Existing tools that predict viral fitness and escape propensities rely heavily on extensive, up-to-date sequence data and lack integration of biochemical host interactions, limiting mechanistic understanding of the mutational landscape. We introduce Esca, a sequence-only toolchain framework that identifies immune escape-prone residues by exhaustively scanning each residue position for all amino acid substitutions using a Bayesian Variational Autoencoder (VAE) trained on protein language model embeddings. We demonstrate Esca on the GP5(ORF5) glycoprotein of PRRSV (EscaPRRS-ORF5) by training on ESM-2 embeddings of 32 146 GP5 sequences (2015-2022) spanning 140 sub-lineages. RESULTS: Despite being trained only on GP5 sequence data, EscaPRRS-ORF5 recovered 85.7% of the surface-exposed receptor binding interfaces as escape-prone regions. We use a mutation-sensitive fitness scoring scheme that goes beyond Hamming distances, to predict antibody escape tendencies, supporting surveillance of (re) emerging PRRSV variants. We do not claim that ORF5 alone captures PRRSV evolution or serves as a surveillance endpoint; rather, Esca offers a scalable path toward whole-genome, structure-aware surveillance. AVAILABILITY AND IMPLEMENTATION: EscaPRRS-ORF5 is freely available at https://doi.org/10.6084/m9.figshare.32661033 with an interactive Colab notebook at https://colab.research.google.com/drive/1TEgzAhPwvNAZ01VXeJbIFibfri2jnDA5? usp=sharing.

Porcine respiratory and reproductive syndrome viru↗
PubMed2025

Robust and accurate Bayesian inference of genome-wide genealogies for hundreds of genomes.

The Ancestral Recombination Graph (ARG), which describes the genealogical history of a sample of genomes, is a vital tool in population genomics and biomedical research. Recent advancements have substantially increased ARG reconstruction scalability, but they rely on approximations that can reduce accuracy, especially under model misspecification. Moreover, they reconstruct only a single ARG topology and cannot quantify the considerable uncertainty associated with ARG inferences. Here, to address these challenges, we introduce SINGER (sampling and inferring of genealogies with recombination), a method that accelerates ARG sampling from the posterior distribution by two orders of magnitude, enabling accurate inference and uncertainty quantification for hundreds of whole-genome sequences. Through extensive simulations, we demonstrate SINGER's enhanced accuracy and robustness to model misspecification compared to existing methods. We demonstrate the utility of SINGER by applying it to individuals of British and African descent within the 1000 Genomes Project, identifying signals of population differentiation, archaic introgression and strong support for ancient polymorphism in the human leukocyte antigen region shared across primates.

Humans↗
PubMed2025

Detecting Interspecific Positive Selection Using Convolutional Neural Networks.

Traditional statistical methods using maximum likelihood and Bayesian inference can detect positive selection from an interspecific phylogeny and a codon sequence alignment based on model assumptions, but they are prone to false positives due to alignment errors and can lack power. These problems are particularly pronounced when faced with high levels of indels and divergence. To address these issues, we trained and tested convolutional neural network models on simulated data and achieved higher accuracy in detecting selection across a specific range of phylogenetic scenarios and evolutionary modes. This advantage is particularly evident when performing inference on noisy data prone to misalignments. Our method shows some ability to account for these errors, where most statistical frameworks fail to do so in a tractable manner. We explore the generalizability of our convolutional neural network models to unseen evolutionary scenarios and identify future avenues to achieve broader utility. Once trained, our convolutional neural network model is faster at test time, making it a scalable alternative to traditional statistical methods for large-scale, multigene analyses. In addition to binary classification (inference of the presence or absence of positive selection during the evolution of the sequences), we use saliency maps to understand what the model learns and observe how this could be leveraged for sitewise inference of positive selection.

Neural Networks, Computer↗
PubMed2025

Bayesian identification of differentially expressed isoforms using a novel joint model of RNA-seq data.

We develop a Bayesian approach, BayesIso, to identify differentially expressed isoforms from RNA-seq data. The approach features a novel joint model of the sample variability and the deferential state of isoforms. Specifically, the within-sample variability and the between-sample variability of each isoform are modeled by a Poisson-Lognormal model and a Gamma-Gamma model, respectively. Using a Bayesian framework, the differential state of each isoform and the model parameters are jointly estimated by a Markov Chain Monte Carlo (MCMC) method. Extensive studies using simulation and real data demonstrate that BayesIso can effectively detect isoforms of less differentially expressed and differential transcripts for genes with multiple isoforms. We applied the approach to breast cancer RNA-seq data and uncovered a unique set of isoforms that form key pathways associated with breast cancer recurrence. First, PI3K/AKT/mTOR signaling and PTEN signaling pathways are identified as being involved in breast cancer development. Further integrated with protein-protein interaction data, pathways of Jak-STAT, mTOR, MAPK and Wnt signaling are revealed in association with breast cancer recurrence. Finally, several pathways are activated in the early recurrence of breast cancer. In tumors that occur early, members of pathways of cellular metabolism and cell cycle (such as CD36 and TOP2A) are upregulated, while immune response genes such as NFATC1 are downregulated.

Humans↗
PubMed2025

Estimating Re and overdispersion in secondary cases from the size of identical sequence clusters of SARS-CoV-2.

The wealth of genomic data that was generated during the COVID-19 pandemic provides an exceptional opportunity to obtain information on the transmission of SARS-CoV-2. Specifically, there is great interest to better understand how the effective reproduction number [Formula: see text] and the overdispersion of secondary cases, which can be quantified by the negative binomial dispersion parameter k, changed over time and across regions and viral variants. The aim of our study was to develop a Bayesian framework to infer [Formula: see text] and k from viral sequence data. First, we developed a mathematical model for the distribution of the size of identical sequence clusters, in which we integrated viral transmission, the mutation rate of the virus, and incomplete case-detection. Second, we implemented this model within a Bayesian inference framework, allowing the estimation of [Formula: see text] and k from genomic data only. We validated this model in a simulation study. Third, we identified clusters of identical sequences in all SARS-CoV-2 sequences in 2021 from Switzerland, Denmark, and Germany that were available on GISAID. We obtained monthly estimates of the posterior distribution of [Formula: see text] and k, with the resulting [Formula: see text] estimates slightly lower than estimates obtained by other methods, and k comparable with previous results. We found comparatively higher estimates of k in Denmark which suggests less opportunities for superspreading and more controlled transmission compared to the other countries in 2021. Our model included an estimation of the case detection and sampling probability, but the estimates obtained had large uncertainty, reflecting the difficulty of estimating these parameters simultaneously. Our study presents a novel method to infer information on the transmission of infectious diseases and its heterogeneity using genomic data. With increasing availability of sequences of pathogens in the future, we expect that our method has the potential to provide new insights into the transmission and the overdispersion in secondary cases of other pathogens.

COVID-19↗
PubMed2026

Quantifying uncertainty of predictions from cancer progression models.

MOTIVATION: Cancer progresses through the accumulation of genomic events. Cancer progression models such as Mutual Hazard Networks (MHNs) describe this dynamic, enabling prediction of temporal event positions and patient-specific risks of acquiring mutations. However, current MHN analyses rely on single most likely models and do not quantify the uncertainty inherent to parameter estimation. Assessing forecast stability is essential before using them to anticipate treatment-relevant mutations, adapt targeted therapies, or prioritize monitoring of patients at elevated progression risk. RESULTS: We address a key prerequisite for the responsible clinical use of cancer progression models by making MHN-derived predictions uncertainty-aware. We present a Bayesian framework for MHN that uses Markov Chain Monte Carlo to sample from the posterior distributions of model parameters and derived predictions. For practical use we implemented the Random-Walk Metropolis, Metropolis-Adjusted Langevin Algorithm (MALA), and simplified manifold MALA samplers as part of the existing mhn Python package. Only MALA and smMALA were successful in sampling from MHN posteriors, with MALA performing best. While most MHN parameters and predictions showed low posterior variance, a small subset displayed greater variability across the posterior distribution. This differentiation cannot be obtained from a single most likely model, emphasizing the need for uncertainty quantification, especially in clinical contexts. As an illustrative example, posterior sampling identified a subgroup of STK11$-$, KRAS$+$ lung adenocarcinoma patients with a high predicted short-term risk-with low variance across posterior samples-to develop an STK11 mutation. This subgroup exhibited poorer survival under immunotherapy, resembling patterns observed in STK11+ patients. AVAILABILITY AND IMPLEMENTATION: Our implementation is part of version 1.2.0 of the mhn package (https://github.com/spang-lab/LearnMHN). All analyses including the code to produce all figures in this article can be found under https://github.com/huy29433/MCMC-sampling-for-MHN (https://doi.org/10.5281/zenodo.21160219).

Humans↗
PubMed2026

Enhancing detection of polygenic adaptation: a comparative study of machine learning and statistical approaches using simulated evolve-and-resequence data.

BACKGROUND: Detecting signals of polygenic adaptation remains a significant challenge in population genomics, as traditional methods often struggle to identify the associated subtle, multi-locus allele-frequency shifts. Here, we introduced and tested several novel approaches combining machine learning techniques with traditional statistical tests to detect polygenic adaptation patterns in time-series of allele frequency changes from whole genome data. We implemented a Naive Bayesian Classifier (NBC) and One-Class Support Vector Machines (OCSVM), and compared their performance against the classical Fisher's Exact Test (FET). Furthermore, we combined machine learning and statistical models (OCSVM-FET and NBC-FET), resulting in 5 competing approaches. The framework is mainly designed and validated for evolve-and-resequence (EaR) experimental designs, where defined selection pressures and temporal sampling are feasible, but might be applicable for certain natural experiments as well. RESULTS: Using a simulated dataset based on empirical C. riparius Pool-Seq data, we evaluated methods across evolutionary scenarios varying in generation, selection strength, and number of loci under selection. Our results demonstrate that the combined OCSVM-FET approach consistently outperformed competing methods, achieving the lowest false positive rate, highest area under the curve, and high accuracy. The performance peak aligned with what we term the 'late dynamic phase' of adaptation - the period after initial selection has occurred but before fixation - highlighting the method's sensitivity to ongoing selective processes. CONCLUSIONS: Furthermore, we emphasize the critical role of parameter tuning, balancing biological assumptions with methodological rigor. While broader applicability remains an important direction for future work, the present benchmarking is intentionally scoped to EaR experimental contexts.

Machine Learning↗
PubMed2026

NExON-Bayes: a Bayesian approach to network estimation informed by ordinal covariates.

MOTIVATION: In heterogeneous disease settings, accounting for intrinsic sample variability is crucial for obtaining reliable and interpretable omic network estimates. However, most graphical model analyses of biomedical data assume homogeneous conditional dependence structures, potentially leading to misleading conclusions. To address this, we propose a joint Gaussian graphical model that leverages sample-level ordinal covariates (e.g. disease stage) to account for heterogeneity and improve the estimation of partial correlation structures. RESULTS: Our modelling framework, called NExON-Bayes, extends the graphical spike-and-slab framework to account for ordinal covariates, jointly estimating their relevance to the graph structure and leveraging them to improve the accuracy of network estimation. To scale to high-dimensional omic settings, we develop an efficient variational inference algorithm tailored to our model. Through simulations, we demonstrate that our method outperforms the vanilla graphical spike-and-slab (with no covariate information), as well as other state-of-the-art network approaches which exploit covariate information. Applying our method to reverse phase protein array data from patients diagnosed with stage I, II or III breast carcinoma, we estimate the behaviour of proteomic networks as cancer progresses. Our model provides insights not only through inspection of the estimated proteomic networks, but also of the estimated ordinal covariate dependencies of key groups of proteins within those networks, offering a comprehensive understanding of how biological pathways shift across disease stages. AVAILABILITY AND IMPLEMENTATION: A user-friendly R package for NExON-Bayes with tutorials is available on Github at github.com/jf687/NExON, and archived at https://doi.org/10.5281/zenodo.20312938. The source of the dataset used is cited in the relevant section.

Bayes Theorem↗