Bayesian Probabilistic Framework Research Articles

IsoBayes : a Bayesian approach for single-isoform proteomics inference.

Studying protein isoforms is an essential step in biomedical research; at present, the main approach for analyzing proteins is via bottom-up mass spectrometry proteomics, which return peptide identifications, that are indirectly used to infer the presence of protein isoforms. However, the detection and quantification processes are noisy; in particular, peptides may be erroneously detected, and most peptides, known as shared peptides, are associated to multiple protein isoforms. As a consequence, studying individual protein isoforms is challenging, and inferred protein results are often abstracted to the gene-level or to groups of protein isoforms. Here, we introduce IsoBayes , a novel statistical method to perform inference at the isoform level. Our method enhances the information available, by integrating mass spectrometry proteomics and transcriptomics data in a Bayesian probabilistic framework. To account for the uncertainty in the measurement process, we propose a two-layer latent variable approach: first, we sample if a peptide has been correctly detected (or, alternatively filter peptides); second, we allocate the abundance of such selected peptides across the protein(s) they are compatible with. This enables us, starting from peptide-level data, to recover protein-level data; in particular, we: i) infer the presence/absence of each protein isoform (via a posterior probability), ii) estimate its abundance (and credible interval), and iii) target isoforms where transcript and protein relative abundances significantly differ. We benchmarked our approach in simulations, and in two multi-protease real datasets: our method displays good sensitivity and specificity when detecting protein isoforms, its estimated abundances highly correlate with the ground truth, and can detect changes between protein and transcript relative abundances. IsoBayes is freely distributed as a Bioconductor R package, and is accompanied by an example usage vignette.

Abstract 792: Continuous, probabilistic variant interpretation with Bayesian graphical models

Abstract Introduction: Current variant classification (VC) frameworks rely on rules-based approaches that use heuristic weighting of various types of evidence, resulting in > 50% of variants being classified as variants of uncertain significance (VUS), and leaving many patients with uncertainty about their disease risk or diagnosis. We propose a probabilistic and scalable Bayesian approach to model the causal relationships between various types of evidence. A fully quantitative system maximizes the utility and integration of various evidence types, empowering clinicians to make more nuanced management decisions. Methods: Probabilistic graphical models (PGMs) are uniquely suited to the needs of clinical VC. Two different component PGMs were developed to model two of the evidence categories that will ultimately be used in a comprehensive VC system: population allele frequency (Population PGM) and reported phenotype observations (Reported Phenotype PGM). Results: The Population PGM treats population allele frequency observations as a binomial process. By conditioning the model on partial observations, the probabilistic relationships between pathogenicity and allele frequencies can be estimated while stochastic variational inference allows uncertainty to be efficiently propagated. The resulting model performs well across a large number of genes at inferring pathogenicity of a variant from its allele frequency, with an average precision of >99% for benign variants. In the Reported Phenotype PGM, phenotypic features characteristic of a disorder are learned from patients expected to be affected based on genotype. Patient-level predictions are in turn combined at the variant level to derive variant pathogenicity likelihoods. To date, models representing at least 102 inherited conditions and 259 genes have demonstrated high predictive performance (>0.8 AUROC) for both patient-level and variant-level predictions. Finally, as a proof-of-concept, we demonstrate how each component PGM can be combined into a probabilistic Bayesian VC framework that also includes protein structure and stability, evolutionary conservation, and sequence context. This framework has high concordance with known, well-accepted pathogenic and benign variants classified with rules-based systems, and could make high-confidence predictions for many variants currently classified as VUS. Conclusion: We present a Bayesian approach that can integrate diverse types of evidence to achieve high VC accuracy while quantifying uncertainty. Future expansion of this Bayesian framework to all evidence types relevant to VC may allow for more accurate risk management guidelines and further inform medical and genetic counseling recommendations. Citation Format: Wolfgang Michael Korn, Yuya Kobayashi, Flavia M. Facio, Arun Nampally, Keith Nykamp, Robert Nussbaum, Alexandre Colavin, Britt Johnson, Toby Manders. Continuous, probabilistic variant interpretation with Bayesian graphical models [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 792.

A Bayesian framework to study tumor subclone-specific expression by combining bulk DNA and single-cell RNA sequencing data.

Genetic and gene expression heterogeneity is an essential hallmark of many tumors, allowing the cancer to evolve and to develop resistance to treatment. Currently, the most commonly used data types for studying such heterogeneity are bulk tumor/normal whole-genome or whole-exome sequencing (WGS, WES); and single-cell RNA sequencing (scRNA-seq), respectively. However, tools are currently lacking to link genomic tumor subclonality with transcriptomic heterogeneity by integrating genomic and single-cell transcriptomic data collected from the same tumor. To address this gap, we developed scBayes, a Bayesian probabilistic framework that uses tumor subclonal structure inferred from bulk DNA sequencing data to determine the subclonal identity of cells from single-cell gene expression (scRNA-seq) measurements. Grouping together cells representing the same genetically defined tumor subclones allows comparison of gene expression across different subclones, or investigation of gene expression changes within the same subclone across time (i.e., progression, treatment response, or relapse) or space (i.e., at multiple metastatic sites and organs). We used simulated data sets, in silico synthetic data sets, as well as biological data sets generated from cancer samples to extensively characterize and validate the performance of our method, as well as to show improvements over existing methods. We show the validity and utility of our approach by applying it to published data sets and recapitulating the findings, as well as arriving at novel insights into cancer subclonal expression behavior in our own data sets. We further show that our method is applicable to a wide range of single-cell sequencing technologies including single-cell DNA sequencing as well as Smart-seq and 10x Genomics scRNA-seq protocols.

FuBay: An Integrated Fusion Framework for Hyperspectral Super-Resolution Based on Bayesian Tensor Ring.

Fusion with corresponding finer-resolution images has been a promising way to enhance hyperspectral images (HSIs) spatially. Recently, low-rank tensor-based methods have shown advantages compared with other kind of ones. However, these current methods either relent to blind manual selection of latent tensor rank, whereas the prior knowledge about tensor rank is surprisingly limited, or resort to regularization to make the role of low rankness without exploration on the underlying low-dimensional factors, both of which are leaving the computational burden of parameter tuning. To address that, a novel Bayesian sparse learning-based tensor ring (TR) fusion model is proposed, named as FuBay. Through specifying hierarchical sprasity-inducing prior distribution, the proposed method becomes the first fully Bayesian probabilistic tensor framework for hyperspectral fusion. With the relationship between component sparseness and the corresponding hyperprior parameter being well studied, a component pruning part is established to asymptotically approaching true latent rank. Furthermore, a variational inference (VI)-based algorithm is derived to learn the posterior of TR factors, circumventing nonconvex optimization that bothers the most tensor decomposition-based fusion methods. As a Bayesian learning methods, our model is characterized to be parameter tuning-free. Finally, extensive experiments demonstrate its superior performance when compared with state-of-the-art methods.

A Bayesian Probabilistic Framework for Building Models for Structural Health Monitoring of Structures Subject to Environmental Variability

A Bayesian Probabilistic Framework for Building Models for Structural Health Monitoring of Structures Subject to Environmental Variability

Bayesian Inversion of Lithology and Liquid Phase Parameters From Seismic Velocity and Electrical Conductivity in the Crust and Uppermost Mantle

AbstractTo deeply understand various geodynamic processes, including volcanic activities and earthquakes, it is essential to extract detailed information about Earth materials, such as lithology and geofluid, from geophysical, petrological, and geochemical observations of Earth's interior. We developed a Bayesian probabilistic framework that can estimate the lithology and geofluid type (aqueous fluid or melt), geofluid amount (porosity), and parameters related to the fluid geometry (aspect ratio and critical fluid fraction related to connectivity) from P‐wave and S‐wave seismic velocities and electrical conductivity data obtained from geophysical tomography. By conducting synthetic inversion tests, we showed that methods based on a joint probability distribution, which simultaneously determines all parameters, sometimes fail to narrow the number of possible answers from 78 lithologies (e.g., basalt, granite, and eclogite) × two geofluid type (melt or aqueous fluid) candidate sets. This failure is derived directly from the difficult nature of inversion problems with relatively large data uncertainties. The proposed method uses a marginalization technique that first estimates lithology and geofluid type and then quantifies geofluid parameter values, which can narrow the probable lithology, geofluid type, and geofluid parameter sets in many cases. In addition, the computational cost of the proposed marginalization method is comparative to a former joint‐estimation method, which is theoretically identical to a previous heuristic method based on the least squares method. Therefore, the marginalization method is useful for geophysical data analyses that involve large amounts of observational data with relatively large uncertainties.

PROBABILISTIC LEARNING OF TREATMENT TREES IN CANCER.

Accurate identification of synergistic treatment combinations and their underlying biological mechanisms is critical across many disease domains, especially cancer. In translational oncology research, preclinical systems such as patient-derived xenografts (PDX) have emerged as a unique study design evaluating multiple treatments administered to samples from the same human tumor implanted into genetically identical mice. In this paper, we propose a novel Bayesian probabilistic tree-based framework for PDX data to investigate the hierarchical relationships between treatments by inferring treatment cluster trees, referred to as treatment trees (Rx-tree). The framework motivates a new metric of mechanistic similarity between two or more treatments accounting for inherent uncertainty in tree estimation; treatments with a high estimated similarity have potentially high mechanistic synergy. Building upon Dirichlet Diffusion Trees, we derive a closed-form marginal likelihood encoding the tree structure, which facilitates computationally efficient posterior inference via a new two-stage algorithm. Simulation studies demonstrate superior performance of the proposed method in recovering the tree structure and treatment similarities. Our analyses of a recently collated PDX dataset produce treatment similarity estimates that show a high degree of concordance with known biological mechanisms across treatments in five different cancers. More importantly, we uncover new and potentially effective combination therapies that confer synergistic regulation of specific downstream biological pathways for future clinical investigations. Our accompanying code, data, and shiny application for visualization of results are available at: https://github.com/bayesrx/RxTree.

Experimental assessment of Bayesian and mode matching approaches for parametric identification of bolted connections

This paper investigates the problem of parametric identification of highly uncertain bolted connections. The unknown parameters representing stiffness of the connections are estimated using two commonly accepted methods: (1) the traditional mode matching approach and (2) a probabilistic Bayesian framework based on the maximum a posteriori (MAP) formulation. Additionally, the uncertainties of the unknown parameters are also estimated and compared for both methods. A numerical example and a real lab-scale frame structure with highly uncertain bolted connections were used in the tests. In the experimental case, the system eigenvalues (squares of the natural frequencies) and the mode shapes measured in a broad frequency range were employed. The measured mode shapes were strongly disturbed by assembly discrepancies of the bolted connections. Finally, both methods were compared in terms of computational efficiency on a large-scale FE model (31,848 degrees of freedom). Despite the sophistication of the Bayesian approach in treating the trade-off between measurement errors and expected modeling errors, the results indicate that the two tested methods yield similar values for the unknown parameters. The Bayesian approach requires numerical regularization to calculate the parameter covariance matrix, which may decrease its reliability. In contrast, the mode matching method avoids such numerical difficulties. Furthermore, the Bayesian approach requires a much larger number of iterations and a careful selection of the weighting parameters.

Is scientific knowledge socially constructed? A Bayesian account of Laboratory Life.

In the book Laboratory Life Latour and Woolgar present an account of how scientific "facts" are formed through a process of microsocial interactions among individuals and "inscription devices" in the lab initially described as social construction. The process moves through a series of steps during which the details and nature of the object become more and more certain until all qualifications are dropped, and the "fact" emerges as secure scientific knowledge. An alternative to this account is described based on a Bayesian probabilistic framework which arrives at the same end point. The motive force for the constructivist approach appears to involve social processes of convincing colleagues while the Bayesian approach relies on the consistency of theory and evidence as judged by the participants. The role of social processes is discussed in Bayesian terms, the acquisition and asymmetry of information, and its analogy to puzzle solving. Some parallels between the Bayesian and constructivist accounts are noted especially in relation to information theory.

Amortized Bayesian Model Comparison With Evidential Deep Learning.

Comparing competing mathematical models of complex processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for guiding decisions. However, many interesting models are intractable with standard Bayesian methods, as they lack a closed-form likelihood function or the likelihood is computationally too expensive to evaluate. In this work, we propose a novel method for performing Bayesian model comparison using specialized deep learning architectures. Our method is purely simulation-based and circumvents the step of explicitly fitting all alternative models under consideration to each observed dataset. Moreover, it requires no hand-crafted summary statistics of the data and is designed to amortize the cost of simulation over multiple models, datasets, and dataset sizes. This makes the method especially effective in scenarios where model fit needs to be assessed for a large number of datasets, so that case-based inference is practically infeasible. Finally, we propose a novel way to measure epistemic uncertainty in model comparison problems. We demonstrate the utility of our method on toy examples and simulated data from nontrivial models from cognitive science and single-cell neuroscience. We show that our method achieves excellent results in terms of accuracy, calibration, and efficiency across the examples considered in this work. We argue that our framework can enhance and enrich model-based analysis and inference in many fields dealing with computational models of natural processes. We further argue that the proposed measure of epistemic uncertainty provides a unique proxy to quantify absolute evidence even in a framework which assumes that the true data-generating model is within a finite set of candidate models.

Robust Bayesian Estimation of EEG-Based Brain Causality Networks.

The multivariate autoregression (MVAR) model is an effective model to construct brain causality networks. However, the accuracy of MVAR parameter estimation is considerably affected by outliers such as head movements and eye blinks contained in EEG signals, especially in short time windows. We proposed a robust MVAR parameter estimation method based on a Bayesian probabilistic framework and Laplace fitting error known as Lap-SBL. With the Bayesian inference framework, we can accurately estimate the MVAR parameters under short time windows. Additionally, to alleviate the influence of outliers, we model the fitting error using the Laplace distribution instead of the typical Gaussian distribution. We employ convex analysis to model the inference task by approximating the Laplace noise prior with a maximum over Gaussian functions with varying scales. The variational inference approach was used to efficiently estimate the MVAR parameters. The numerical results suggest that the proposed method obtains less parameter estimation bias and more consistent linkages than existing benchmark methods, i.e., LS, LASSO, LAPPS and SBL. The motor imagery experimental data analysis shows that Lap-SBL can better describe the lateralization characteristics of brain network. This lateralization is less apparent in a subject with poor MI classification accuracy. Lap-SBL effectively suppresses the influence of outliers and recovers reliable networks in the presence of outliers and short time windows.

Bayesian Collaborative Learning for Whole-Slide Image Classification.

Whole-slide image (WSI) classification is fundamental to computational pathology, which is challenging in extra-high resolution, expensive manual annotation, data heterogeneity, etc. Multiple instance learning (MIL) provides a promising way towards WSI classification, which nevertheless suffers from the memory bottleneck issue inherently, due to the gigapixel high resolution. To avoid this issue, the overwhelming majority of existing approaches have to decouple the feature encoder and the MIL aggregator in MIL networks, which may largely degrade the performance. Towards this end, this paper presents a Bayesian Collaborative Learning (BCL) framework to address the memory bottleneck issue with WSI classification. Our basic idea is to introduce an auxiliary patch classifier to interact with the target MIL classifier to be learned, so that the feature encoder and the MIL aggregator in the MIL classifier can be learned collaboratively while preventing the memory bottleneck issue. Such a collaborative learning procedure is formulated under a unified Bayesian probabilistic framework and a principled Expectation-Maximization algorithm is developed to infer the optimal model parameters iteratively. As an implementation of the E-step, an effective quality-aware pseudo labeling strategy is also suggested. The proposed BCL is extensively evaluated on three publicly available WSI datasets, i.e., CAMELYON16, TCGA-NSCLC and TCGA-RCC, achieving an AUC of 95.6%, 96.0% and 97.5% respectively, which consistently outperforms all the methods compared. Comprehensive analysis and discussion will also be presented for in-depth understanding of the method. To promote future work, our source code is released at: https://github.com/Zero-We/BCL.

Estimating vadose zone water fluxes from soil water monitoring data: a comprehensive field study in Austria

Abstract. Groundwater recharge is a key component of the hydrological cycle, yet its direct measurement is complex and often difficult to achieve. An alternative is its inverse estimation through a combination of numerical models and transient observations from distributed soil water monitoring stations. However, an often neglected aspect of this approach is the effect of model predictive uncertainty on simulated water fluxes. In this study, we made use of long-term soil water content measurements at 14 locations from the Austrian soil water monitoring program to quantify and compare local potential groundwater recharge rates and their temporal variability. Observations were coupled with a Bayesian probabilistic framework to calibrate the HYDRUS-1D model and assess the effect of model predictive uncertainty on long-term simulated recharge fluxes. Estimated annual potential recharge rates ranged from 44 to 1319 mm a−1 with a relative uncertainty (95 % interquantile range/median) in the estimation of between 1 % and 39 %. Recharge rates decreased longitudinally, with high rates and lower seasonality at western sites and low rates with high seasonality and extended periods without recharge at the southeastern and eastern Austrian sites. Higher recharge rates and lower actual evapotranspiration were related to sandy soils; however, climatic factors had a stronger influence on estimated potential groundwater recharge than soil properties, underscoring the vulnerability of groundwater recharge to the effects of climate change.

Bayesian selection of plane-wave decomposition models.

Plane-wave decompositions, whereby a measured sound field is described as a superposition of plane waves, are central to many applications in acoustics and audio engineering. This letter applies a Bayesian probabilistic inference framework to the plane wave decomposition problem and examines the Deviance Information Criterion (DIC) for selecting the optimum number of waves in the decomposition. The framework learns the model directly from the data and, as such, adapts to the wavefield under study. The DIC is applied to data measured in two reverberant sound fields (highly-reverberant and lightly-damped) to determine the simplest models providing the preferred fit to the data.

Uncertainty Quantification in Constitutive Models of Highway Bridge Components: Seismic Bars and Elastomeric Bearings

Bridges are essential structures in the logistic chain of countries, making it critical to design them to be as resilient as possible. One way to achieve this is through performance-based seismic design (PBSD), which involves using nonlinear Finite Element (FE) models to predict the response and potential damage of different structural components under earthquake excitations. Nonlinear FE models need accurate constitutive models of material and components. Among them, seismic bars and laminated elastomeric bearings play an important role in a bridge's response to earthquakes; therefore, properly validated and calibrated models should be proposed. Only default parameter values from the early development of the constitutive models widely used by researchers and practitioners for these components tend to be used, and low identifiability of its governing parameters and the high cost of generating reliable experimental data have prevented a thorough probabilistic characterization of their model parameters. To address this issue, this study implements a Bayesian probabilistic framework using Sequential Monte Carlo (SMC) for updating the parameters of constitutive models of seismic bars and elastomeric bearings and proposes joint probability density functions (PDF) for the most influential parameters. The framework is based on actual data from comprehensive experimental campaigns. The PDFs are obtained from independent tests conducted on different seismic bars and elastomeric bearings, to then consolidate all the information in a single PDF for each modeling parameter by means of the conflation methodology, where the mean, coefficient of variation, and correlation between calibrated parameters are obtained for each bridge component. Finally, findings show that the incorporation of model parameter uncertainty through a probabilistic framework will allow for a more accurate prediction of the response of bridges under strong earthquakes.

A Bayesian Probabilistic Framework for Identification of Individuals with Dyslexia

ABSTRACT Purpose Bayesian-based models for diagnosis are common in medicine but have not been incorporated into identification models for dyslexia. The purpose of the present study was to evaluate Bayesian identification models that included a broader set of predictors and that capitalized on recent developments in modeling the prevalence of dyslexia. Method Model-based meta-analysis was used to create a composite correlation matrix that included common predictors of dyslexia such as decoding, phonological awareness, oral language, but also included response to intervention (RTI) and family risk for dyslexia. Bayesian logistic regression models were used to predict poor reading comprehension, unexpectedly poor reading comprehension, poor decoding, and unexpectedly poor decoding, all at two levels of severity. Results Most predictors made independent and substantial contributions to prediction, supporting models of dyslexia that rely on multiple rather than single indicators. RTI was the strongest predictor of poor reading comprehension and unexpectedly poor reading comprehension. Phonological awareness was the strongest predictor of poor decoding and unexpectedly poor decoding, followed closely by family risk. Conclusion Bayesian-based models are a promising tool for implementing multiple-indicator models of identification. Ideas for improving prediction and implications for theory and practice are discussed.

A new Bayesian probabilistic integration framework for hybrid uncertainty propagation

Efficient propagation of uncertainty is one of the most critical tasks for uncertainty quantification and reliable design in the presence of multi-source uncertainties. This work presents a new methodology framework, termed as “mixed imprecise probabilistic integration”, for efficient propagation of the uncertainties characterized by non-probabilistic models, imprecise probability models and precise probability models. In this paper, the mixed-high dimensional model representation combining the cut-high dimensional model representation and random sampling-high dimensional model representation is firstly proposed, which conserves all the advantages of these two methods. Secondly, the proposed method is realized by using mixed-high dimensional model representation and Bayesian inference. The estimations and the posterior variances of the proposed method are analytically derived of high accuracy. With the proposed method, all the three kinds of uncertainty models can be efficiently propagated with one set of function evaluations. The effectiveness of the proposed methods is demonstrated by three engineering examples.

How Does Multiverse Proposal Affect the Design Argument?

Recent observations suggest that many fundamental physical constants and conditions in our universe are fine-tuned for life to exist. This provides an important piece of evidence to support the Design Argument and the existence of God in the philosophy of religion. However, the proposal of multiverse provides a naturalistic account of the fine-tuning phenomena which apparently challenges the Design Argument. In general, most of the multiverse models have specific features and they have to satisfy empirical and logical constraints. Therefore, they may be intrinsically dependent on theistic proposal under the probabilistic Bayesian framework. In this article, I present a Bayesian framework to show how multiverse proposal affects the Design Argument. I show that there exist two specific scenarios in which the inclusion of multiverse proposal can indirectly increase the credence of the Design Argument.

A probabilistic data assimilation framework to reconstruct finite element error fields from sparse error estimates: Application to sub‐modeling

AbstractThe present work proposes a computational approach that recovers full finite element error fields from a small number of estimates of errors in scalar quantities of interest. The approach is weakly intrusive and is motivated by large scale industrial applications wherein modifying the finite element models is undesirable and multiple regions of interest may exist in a single model. Error estimates are developed using a Zhu‐Zienkiewicz estimator coupled with the adjoint methodology to deliver goal‐oriented results. A Bayesian probabilistic estimation framework is deployed for full field estimation. An adaptive, radial basis function based reduced order modeling strategy is implemented to reduce the cost of calculating the posterior. The Bayesian reconstruction approach, accelerated by the proposed model reduction technology, is shown to yield good probabilistic estimates of full error fields, with a computational complexity that is acceptable compared to the evaluation of the goal‐oriented error estimates. The novelty of the work is that a set of computed error estimates are considered as partial observations of an underlying error field, which is to be recovered. Future improvements of the method include the optimal selection of goal‐oriented error measures to be acquired prior to the error field reconstruction.

A novel probabilistic regression model for electrical peak demand estimate of commercial and manufacturing buildings

Due to the high cost of electricity in commercial and industrial sectors, demand forecast models have gained increasing attention. However, there are two unresolved issues: (1) Models are not adaptable when exposed to previously unknown data (2) The value of regression methods vs. state-of-the-art machine learning models has not been made apparent before. This study’s goal is to develop probabilistic demand estimation models. We propose a probabilistic Bayesian regression framework that can not only estimate future demands with high accuracy but also be updated once new information is available. By applying the proposed algorithm to two real-world case studies (commercial and manufacturing), we show a 40.3% and 30.8% improvement in terms of mean absolute error for the two cases. Moreover, the proposed technique outperforms powerful machine learning approaches, including support vector machine by 10.39%, random forest by 6.17%, and multilayer perceptron by 9.14% in terms of mean absolute percentage error.