Bayesian Probabilistic Framework Research Articles

Bayesian probabilistic representation of complex systems: With application to wave load modeling

AbstractIn this contribution, we develop and present a Bayesian probabilistic framework for the representation of complex systems and apply this to an industrial case of offshore environmental load modeling. Based on previous contributions on probabilistic modeling using Bayesian networks, we consider the case where both the model structure and its parameters are estimated from data. Gaussian process‐based discrepancy modeling is introduced to represent uncertainties associated with data, when data are produced by models themselves. Two approaches are then introduced on how to deal with multiple model candidates, that is, Bayesian model averaging and decision context‐specific model selection. The latter comprising the main novelty of this paper. Two examples are provided: (i) a principal example illustrating the simple but fundamental idea of context‐specific model building and (ii) an industrial‐scale example considering optimal ranking of evacuation options for platform personnel in the event of an emerging storm.

A Bayesian method for synthesizing multiple diagnostic outcomes of COVID-19 tests

The novel coronavirus disease 2019 (COVID-19) has spread worldwide and threatened human life. Diagnosis is crucial to contain the spread of SARS-CoV-2 infections and save lives. Diagnostic tests for COVID-19 have varying sensitivity and specificity, and the false-negative results would have substantial consequences to patient treatment and pandemic control. To detect all suspected infections, multiple testing is widely used. However, it may be challenging to build an assertion when the testing results are inconsistent. Considering the situation where there is more than one diagnostic outcome for each subject, we proposed a Bayesian probabilistic framework based on the sensitivity and specificity of each diagnostic method to synthesize a posterior probability of being infected by SARS-CoV-2. We demonstrated that the synthesized posterior outcome outperformed each individual testing outcome. A user-friendly web application was developed to implement our analytic framework with free access via http://www2.ccrb.cuhk.edu.hk/statgene/COVID_19/. The web application enables the real-time display of the integrated outcome incorporating two or more tests and calculated based on Bayesian posterior probability. A simulation-based assessment demonstrated higher accuracy and precision of the Bayesian probabilistic model compared with a single-test outcome. The online tool developed in this study can assist physicians in making clinical evaluations by effectively integrating multiple COVID-19 tests.

Observer control for bearings-only tracking using possibility functions

Bearings-only tracking using passive sensors is important for covert surveillance of moving targets. This paper adopts a mathematical formulation of bearings-only tracking in the framework of possibility theory, where uncertainties are represented using possibility functions, rather than usual probability distributions. Possibility functions have the capacity to deal robustly with partial (incomplete) specification of mathematical models and have been found particularly useful in model mismatch situations. The paper explores the design of reward functions which provide information gain in the context of observer motion control, in the framework of possibilistic recursive filter for bearings-only tracking. Numerical results demonstrate that in the presence of a model mismatch, the proposed framework performs better than the Bayesian probabilistic framework for stochastic filtering and control.

A novel multiscale biophysical model to predict the fate of ionizable compounds in the soil-plant continuum

Soil pollution from emerging contaminants poses a significant threat to water resources management and food production. The development of numerical models to describe the reactive transport of chemicals in both soil and plant is of paramount importance to elaborate mitigation strategies. To this aim, in the present study, a multiscale biophysical model is developed to predict the fate of ionizable compound in the soil-plant continuum. The modeling framework connects a multi-organelles model to describe processes at the cell level with a semi-mechanistic soil-plant model, which includes the widely used Richards-based solver, HYDRUS. A Bayesian probabilistic framework is used to calibrate and assess the capability of the model in reproducing the observations from an experiment on the translocation of five pharmaceuticals in green pea plants. Results show satisfactory fitting performance and limited predictive uncertainty. The subsequent validation with the cell model indicates that the estimated soil-plant parameters preserve a physically realistic meaning, and their calibrated values are comparable with the existing literature values, thus confirming the overall reliability of the analysis. Model results further suggest that pH conditions in both soil and xylem play a crucial role in the uptake and translocation of ionizable compounds.

Seropositivity in blood donors and pregnant women during the first year of SARS-CoV-2 transmission in Stockholm, Sweden.

BackgroundIn Sweden, social restrictions to contain SARS‐CoV‐2 have primarily relied upon voluntary adherence to a set of recommendations. Strict lockdowns have not been enforced, potentially affecting viral dissemination. To understand the levels of past SARS‐CoV‐2 infection in the Stockholm population before the start of mass vaccinations, healthy blood donors and pregnant women (n = 5,100) were sampled at random between 14 March 2020 and 28 February 2021.MethodsIn this cross‐sectional prospective study, otherwise‐healthy blood donors (n = 2,600) and pregnant women (n = 2,500) were sampled for consecutive weeks (at four intervals) throughout the study period. Sera from all participants and a cohort of historical (negative) controls (n = 595) were screened for IgG responses against stabilized trimers of the SARS‐CoV‐2 spike (S) glycoprotein and the smaller receptor‐binding domain (RBD). As a complement to standard analytical approaches, a probabilistic (cut‐off independent) Bayesian framework that assigns likelihood of past infection was used to analyse data over time.SettingHealthy participant samples were randomly selected from their respective pools through Karolinska University Hospital. The study was carried out in accordance with Swedish Ethical Review Authority: registration number 2020–01807.ParticipantsNo participants were symptomatic at sampling, and blood donors were all over the age of 18. No additional metadata were available from the participants.ResultsBlood donors and pregnant women showed a similar seroprevalence. After a steep rise at the start of the pandemic, the seroprevalence trajectory increased steadily in approach to the winter second wave of infections, approaching 15% of all individuals surveyed by 13 December 2020. By the end of February 2021, 19% of the population tested seropositive. Notably, 96% of seropositive healthy donors screened (n = 56) developed neutralizing antibody responses at titres comparable to or higher than those observed in clinical trials of SARS‐CoV‐2 spike mRNA vaccination, supporting that mild infection engenders a competent B‐cell response.ConclusionsThese data indicate that in the first year since the start of community transmission, seropositivity levels in metropolitan in Stockholm had reached approximately one in five persons, providing important baseline seroprevalence information prior to the start of vaccination.

Prediction of regional wildfire activity in the probabilistic Bayesian framework of Firelihood.

Modeling wildfire activity is crucial for informing science-based risk management and understanding the spatiotemporal dynamics of fire-prone ecosystems worldwide. Models help disentangle the relative influences of different factors, understand wildfire predictability, and provide insights into specific events. Here, we develop Firelihood, a two-component, Bayesian, hierarchically structured, probabilistic model of daily fire activity, which is modeled as the outcome of a marked point process: individual fires are the points (occurrence component), and fire sizes are the marks (size component). The space-time Poisson model for occurrence is adjusted to gridded fire counts using the integrated nested Laplace approximation (INLA) combined with the stochastic partial differential equation (SPDE) approach. The size model is based on piecewise-estimated Pareto and generalized Pareto distributions, adjusted with INLA. The Fire Weather Index (FWI) and forest area are the main explanatory variables. Temporal and spatial residuals are included to improve the consistency of the relationship between weather and fire occurrence. The posterior distribution of the Bayesian model provided 1,000 replications of fire activity that were compared with observations at various temporal and spatial scales in Mediterranean France. The number of fires larger than 1ha across the region was coarsely reproduced at the daily scale, and was more accurately predicted on a weekly basis or longer. The regional weekly total number of larger fires (10-100ha) was predicted as well, but the accuracy degraded with size, as the model uncertainty increased with event rareness. Local predictions of fire numbers or burned areas also required a longer aggregation period to maintain model accuracy. The estimation of fires larger than 1ha was also consistent with observations during the extreme fire season of the 2003 unprecedented heat wave, but the model systematically underrepresented large fires and burned areas, which suggests that the FWI does not consistently rate the actual danger of large fire occurrence during heat waves. Firelihood enabled a novel analysis of the stochasticity underlying fire hazard, and offers a variety of applications, including fire hazard predictions for management and projections in the context of climate change.

Variational Bayesian probabilistic modeling framework for data-driven distributed process monitoring

Data-driven process monitoring has gained increasing attention because of the increasing demand in process safety and the rapid advancement of data gathering techniques. When monitoring a plant-wide multiunit process, establishing a monitor for each unit individually ignores the correlations among units, whereas establishing a global monitor for the entire process ignores the local process behavior. A variational Bayesian-based probabilistic modeling approach is proposed for efficient distributed process monitoring. A novel probabilistic latent variable model is developed to characterize the variable relationship in each local unit and among units. First, variational Bayesian-based latent variable extraction is performed in each local unit, through which variable relationship within a local unit is characterized. Second, variational Bayesian-based regression model is established between the latent variables and neighboring variables, through which the variable relationship among units is characterized. Then, modeling residuals and monitoring statistics are generated, through which the process status and the type of a detected fault are identified. The effectiveness of the proposed probabilistic modeling and monitoring method is verified by three case studies, including a numerical example, the Tennessee Eastman benchmark process, and a laboratory distillation process.

A probabilistic Bayesian framework to deal with the uncertainty in hydro-climate projection of Zayandeh-Rud River Basin

Different sources of uncertainty exist in climate change impacts projection. This study aims to propose a framework to deal with the various sources of uncertainties involved in hydro-climate projections of Zayandeh-Rud River Basin with area of 26,917 km2 in Central Iran. The Bayesian model averaging (BMA) was here used through two distinct approaches for weighting the hydrologic outputs (App. I) as well as the global climate models (GCMs) (App. II) based on their abilities to simulate the baseline period. The results showed that different GCMs have different abilities in estimating the hydro-climatic variables and the application of uncertainty analysis is necessary for climate change studies. Application of the BMA can significantly reduce the errors in historical runoff prediction. Although App. I showed a better performance of generating the stream flow time series during the baseline period, the App. II approach has an acceptable ability in different months. The findings of flow duration curves under both approaches revealed that App. II is more appropriate to deal with uncertainty of hydro-climate projection especially in arid and semi-arid regions.

On the Use of Mechanistic Soil-Plant Uptake Models: A Comprehensive Experimental and Numerical Analysis on the Translocation of Carbamazepine in Green Pea Plants.

Food contamination is a major worldwide risk for human health. Dynamic plant uptake of pollutants from contaminated environments is the preferred pathway into the human and animal food chain. Mechanistic models represent a fundamental tool for risk assessment and the development of mitigation strategies. However, difficulty in obtaining comprehensive observations in the soil–plant continuum hinders their calibration, undermining their generalizability and raising doubts about their widespread applicability. To address these issues, a Bayesian probabilistic framework is used, for the first time, to calibrate and assess the predictive uncertainty of a mechanistic soil–plant model against comprehensive observations from an experiment on the translocation of carbamazepine in green pea plants. Results demonstrate that the model can reproduce the dynamics of water flow and solute reactive transport in the soil–plant domain accurately and with limited uncertainty. The role of different physicochemical processes in bioaccumulation of carbamazepine in fruits is investigated through Global Sensitivity Analysis, which shows how soil hydraulic properties and soil solute sorption regulate transpiration streams and bioavailability of carbamazepine. Overall, the analysis demonstrates the usefulness of mechanistic models and proposes a comprehensive numerical framework for their assessment and use.

Abstract 40: scBayes: A computational method to study tumor subclone-specific gene expression and chromatin accessibility using single-cell RNA sequencing and single-cell ATAC sequencing in combination of bulk DNA sequencing

Abstract Although critical for understanding the underlying cancer biology, the study of tumor cell phenotype and epigenetic state from bulk gene expression (RNA-seq) and chromatin accessibility (ATAC-seq) data is often challenging because tumor samples are typically mixtures of different cell populations due to normal tissue contamination, immune cell infiltration, and tumor subclonality. These cell populations may have vastly divergent transcriptomic and epigenetic characteristics, resulting in mixtures of signals that are often impossible to deconvolute. Here we present scBayes, a computational method that allows one to characterize the transcriptional behavior and/or epigenetic state corresponding to each tumor subclone present in a tumor sample or multiple serial or multisite samples from a given cancer patient. This tool starts with genomically defined subclones reconstructed from bulk DNA sequencing data, e.g., using our own published SubcloneSeeker algorithm. scBayes then layers single-cell gene expression (scRNA-seq) and/or chromatin accessibility (scATAC-seq) data on this genomic subclone “backbone” to assign individual cells to one of the tumor subclones or normal cell compartment, facilitating subclone-specific expression or epigenetic analysis. This allows (1) the identification of tumor expression or epigenetic signals without normal tissue interference, (2) the comparison between tumor and normal cells from the same sample, (3) the comparison of expression and epigenetic state across distinct tumor subclones, and (4) the study of transcriptional/epigenetic plasticity through the comparison of the cell states of the same genomically defined subclone across different time points or metastatic sites. scBayes achieves cell-to-subclone assignment by assessing the presence of somatic variants (CNVs or SNVs) that define cancer subclones in each individual cell from the single-cell sequencing reads. Because per-cell sequencing coverage is sparse, and therefore variant dropout frequent, scBayes utilizes a Bayesian probabilistic framework to calculate the likelihood of a particular cell originating from each subclone (including the normal clone, defined as having no somatic mutations) and makes a probabilistic assignment, maximizing the utilization of the sparse single-cell sequencing data for subclone assignment. We successfully applied this method to multiple longitudinal and metastatic cancer patient datasets, representing both bulk WES and WGS DNA sequencing, as well as single-cell datasets collected using the 10X Chromium and Fluidigm C1 platforms. Our algorithmic approach enables comparative gene expression and pathway analysis, and open chromatin accessibility assessment, across subclones. scBayes is open source and freely available at https://github.com/yiq/scBayes. Citation Format: Yi Qiao, Xiaomeng Huang, Gabor Marth. scBayes: A computational method to study tumor subclone-specific gene expression and chromatin accessibility using single-cell RNA sequencing and single-cell ATAC sequencing in combination of bulk DNA sequencing [abstract]. In: Proceedings of the AACR Special Conference on Advancing Precision Medicine Drug Development: Incorporation of Real-World Data and Other Novel Strategies; Jan 9-12, 2020; San Diego, CA. Philadelphia (PA): AACR; Clin Cancer Res 2020;26(12_Suppl_1):Abstract nr 40.

DISCOVERING CAUSALITIES FROM CARDIOTOCOGRAPHY SIGNALS USING IMPROVED CONVERGENT CROSS MAPPING WITH GAUSSIAN PROCESSES.

Convergent cross mapping (CCM) is designed for causal discovery in coupled time series, where Granger causality may not be applicable because of a separability assumption. However, CCM is not robust to observation noise which limits its applicability on signals that are known to be noisy. Moreover, the parameters for state space reconstruction need to be selected using grid search methods. In this paper, we propose a novel improved version of CCM using Gaussian processes for discovery of causality from noisy time series. Specifically, we adopt the concept of CCM and carry out the key steps using Gaussian processes within a non-parametric Bayesian probabilistic framework in a principled manner. The proposed approach is first validated on simulated data, and then used for understanding the interaction between fetal heart rate and uterine activity in the last two hours before delivery and of interest in obstetrics. Our results indicate that uterine activity affects the fetal heart rate, which agrees with recent clinical studies.

A Bayesian Approach to the Naming Game Model

We present a novel Bayesian approach to semiotic dynamics, which is a cognitive analog of the naming game model restricted to two conventions. The model introduced in this paper provides a general framework for studying the combined effects of cognitive and social dynamics. The one-shot learning that characterizes the agent dynamics in the basic naming game is replaced by a word-learning process in which agents learn a new word by generalizing from the evidence garnered through pairwise-interactions with other agents. The principle underlying the model is that agents—like humans—can learn from a few positive examples and that such a process is modeled in a Bayesian probabilistic framework. We show that the model presents some analogies with the basic two-convention naming game model but also some relevant differences in the dynamics, which we explain through a geometric analysis of the mean-field equations.

BayesMallows: An R Package for the Bayesian Mallows Model

BayesMallows is an R package for analyzing data in the form of rankings or preferences with the Mallows rank model, and its finite mixture extension, in a Bayesian probabilistic framework. The Mallows model is a well-known model, grounded on the idea that the probability density of an observed ranking decreases exponentially fast as its distance to the location parameter increases. Despite the model being quite popular, this is the first Bayesian implementation that allows a wide choice of distances, and that works well with a large amount of items to be ranked. BayesMallows supports footrule, Spearman, Kendall, Cayley, Hamming and Ulam distances, allowing full use of the rich expressiveness of the Mallows model. This is possible thanks to the implementation of fast algorithms for approximating the partition function of the model under various distances. Although developed for being used in computing the posterior distribution of the model, these algorithms may be of interest in their own right. BayesMallows handles non-standard data: partial rankings and pairwise comparisons, even in cases including non-transitive preference patterns. The advantage of the Bayesian paradigm in this context comes from its ability to coherently quantify posterior uncertainties of estimates of any quantity of interest. These posteriors are fully available to the user, and the package comes with convienient tools for summarizing and visualizing the posterior distributions.

Detecting Causality using Deep Gaussian Processes.

Convergent cross mapping (CCM) is a state space reconstruction (SSR)-based method designed for causal discovery in coupled time series, where Granger causality may not be applicable due to a separability assumption. However, CCM requires a large number of observations and is not robust to observation noise which limits its applicability. Moreover, in CCM and its variants, the SSR step is mostly implemented with delay embedding where the parameters for reconstruction usually need to be selected using grid search-based methods. In this paper, we propose a Bayesian version of CCM using deep Gaussian processes (DGPs), which are naturally connected with deep neural networks. In particular, we adopt the framework of SSR-based causal discovery and carry out the key steps using DGPs within a non-parametric Bayesian probabilistic framework in a principled manner. The proposed approach is first validated on simulated data and then tested on data used in obstetrics for monitoring the well-being of fetuses, i.e., fetal heart rate (FHR) and uterine activity (UA) signals in the last two hours before delivery. Our results indicate that UA affects the FHR, which agrees with recent clinical studies.

A probabilistic framework to incorporate mixed-data type features: Matrix factorization with multimodal side information

Recommender systems that exclusively rely on past interactions between the users and the items underperform in settings with very few observations. Their performance at such extreme sparsity can be improved by exploiting the side information of the users and the items including the demographics and the item descriptions. However, such side information is mostly heterogeneous and multimodal, including both numerical and categorical features to yield a non-trivial incorporation process. Researchers have addressed this problem mainly by converting the categorical features into numerical ones or forming numerical similarity matrices. This paper presents a different approach in the form of a novel Bayesian probabilistic generative framework which can effectively incorporate multimodal side information into the matrix factorization (MF-MSI) model. With the help of local quadratic bounds on the categorical likelihoods, we derive a scalable and computationally efficient iterative optimization method based on the variational EM to learn the posterior distributions of latent variables for both the users and the items. A comprehensive experimental study on both simulated and real benchmark datasets demonstrate the proof-of-concept where the additional side information improves both the prediction accuracy and the ranking performance over more than a dozen popular baseline models. Finally, the proposed MF-MSI model claims state-of-the-art performance in the majority of the test scenarios when compared to more recently introduced recommender systems which can also utilize the side information via different techniques.

Bayesian Deep Collaborative Matrix Factorization

In this paper, we propose a Bayesian Deep Collaborative Matrix Factorization (BDCMF) algorithm for collaborative filtering (CF). BDCMF is a novel Bayesian deep generative model that learns user and item latent vectors from users’ social interactions, contents of items as the auxiliary information and user-item rating (feedback) matrix. It alleviates the problem of matrix sparsity by incorporating items’ auxiliary and users’ social information into the model. It can learn more robust and dense latent representations by integrating deep learning into Bayesian probabilistic framework. As being one of deep generative models, it has both non-linearity and Bayesian nature. Additionally, in BDCMF, we derive an efficient EM-style point estimation algorithm for parameter learning. To further improve recommendation performance, we also derive a full Bayesian posterior estimation algorithm for inference. Experiments conducted on two sparse datasets show that BDCMF can significantly outperform the state-of-the-art CF methods.

Abstract 4689: Subclone-specific evolution of tumor phenotypes – A framework to study subclone-specific gene expression from a combination of bulk DNA and single cell RNA sequencing data

Abstract Several approaches are now available for subclonal reconstruction of heterogeneous tumor biopsies from somatic variant allele frequencies measured in bulk DNA sequencing datasets, including our own SubcloneSeeker program. However, to understand how chemoresistance, relapse, or metastasis evolves at a subclonal level, we also need to study the molecular phenotype corresponding to each subclone. Single-cell RNAseq technologies now allow one to study the transcriptomic characteristics and phenotypic behaviors of individual cells, but new algorithms are needed to link these cells to the genomically defined tumor subclones they represent. Here we present a computational approach to make such cell assignments, using a combination of bulk DNA sequencing data (WGS or WES), and single cell RNA sequencing (scRNAseq) collected from the same tissues. Subclones constructed from bulk DNA sequencing data are defined by specific combinations of somatic mutations (SNVs and CNVs). Our algorithm uses the scRNA-seq reads to assess which of these subclone-defining mutations are present in each individual cell, then utilizes a Bayesian probabilistic framework for making the cell-to-subclone assignment. This framework overcomes the challenges of sparse scRNA-seq read coverage, and maximizes the accuracy and efficiency of cell assignment. We have successfully applied this method to multiple longitudinal and metastatic cancer patient datasets, representing both WES and WGS bulk DNA sequencing, as well as datasets collected using the 10X Chromium and Fluidigm C1 technologies. Our algorithm uses both somatically acquired CNV and SNV events in the tumor for cell assignment. Using our approach, as many of 80% of tumor cells could be assigned to specific subclones, enabling comparative gene expression and pathway analysis across subclones. Citation Format: Yi Qiao, Xiaomeng Huang, Samuel Brady, Andrea Bild, David Bowtell, William Johnson, Gabor Marth. Subclone-specific evolution of tumor phenotypes – A framework to study subclone-specific gene expression from a combination of bulk DNA and single cell RNA sequencing data [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 4689.

A hierarchical autoencoder learning model for path prediction and abnormality detection

In this paper, we introduce an unsupervised hierarchical framework for modeling trajectories in surveillance scenarios. Inspired by the object recognition field, a novel feature representation optimized for a neural network learning architecture is proposed. Low levels of the hierarchy capture local spatio-temporal motion attributes such as spatial orientation and speed, while higher levels contribute to obtaining richer semantic information. The bottom-up construction of the hierarchical framework exploits the inherent statistical correlations between neighboring elements using an increasing spatio-temporal grid. Cross-entropy based optimization in combination with autoencoders is used to learn weights for subsequent hierarchical layers. Finally, the Bayesian probabilistic framework built on top of the hierarchical model is proposed for applications such as long-term path prediction and abnormality detection. We demonstrate the efficiency of the proposed model on both indoor and outdoor datasets, achieving results comparable with state-of-the-art methods.

A Deep Bayesian Tensor-Based System for Video Recommendation

With the availability of abundant online multi-relational video information, recommender systems that can effectively exploit these sorts of data and suggest creatively interesting items will become increasingly important. Recent research illustrates that tensor models offer effective approaches for complex multi-relational data learning and missing element completion. So far, most tensor-based user clustering models have focused on the accuracy of recommendation. Given the dynamic nature of online media, recommendation in this setting is more challenging as it is difficult to capture the users’ dynamic topic distributions in sparse data settings as well as to identify unseen items as candidates of recommendation. Targeting at constructing a recommender system that can encourage more creativity, a deep Bayesian probabilistic tensor framework for tag and item recommendation is proposed. During the score ranking processes, a metric called Bayesian surprise is incorporated to increase the creativity of the recommended candidates. The new algorithm, called Deep Canonical PARAFAC Factorization (DCPF), is evaluated on both synthetic and large-scale real-world problems. An empirical study for video recommendation demonstrates the superiority of the proposed model and indicates that it can better capture the latent patterns of interactions and generates interesting recommendations based on creative tag combinations.

Bayesian framework for elastic full-waveform inversion with facies information

Conventional reservoir-characterization techniques utilize amplitude-variation-with-offset (AVO) analysis to invert for the elastic parameters or directly for the physical properties of reservoirs. However, the quality of AVO inversion is degraded by errors in the velocity model, inaccurate amplitudes, and structural complexity. Whereas full-waveform inversion (FWI) potentially represents a much more powerful tool for reservoir characterization. FWI strongly relies on the accuracy of the initial model and suffers from parameters trade-offs. Here, we use a probabilistic Bayesian framework to supplement data fitting with rock-physics constraints based on geologic facies obtained from borehole information (well logs). The advantages of the facies-based FWI are demonstrated on a structurally complex isotropic elastic model and on a 3D layered VTI (transversely isotropic with a vertical symmetry axis) medium. In particular, the tests show that our algorithm can operate without ultra-low-frequency data required by conventional FWI and can reduce crosstalk between the medium parameters.