Discovering gene regulatory networks of multiple phenotypic groups using dynamic Bayesian networks.

Dynamic Bayesian networks (DBNs) can be used for the discovery of gene regulatory networks (GRNs) from time series gene expression data. Here, we suggest a strategy for learning DBNs from gene expression data by employing a Bayesian approach that is scalable to large networks and is targeted at learning models with high predictive accuracy. Our framework can be used to learn DBNs for multiple groups of samples and highlight differences and similarities in their GRNs. We learn these DBN models based on different structural and parametric assumptions and select the optimal model based on the cross-validated predictive accuracy. We show in simulation studies that our approach is better equipped to prevent overfitting than techniques used in previous studies. We applied the proposed DBN-based approach to two time series transcriptomic datasets from the Gene Expression Omnibus database, each comprising data from distinct phenotypic groups of the same tissue type. In the first case, we used DBNs to characterize responders and non-responders to anti-cancer therapy. In the second case, we compared normal to tumor cells of colorectal tissue. The classification accuracy reached by the DBN-based classifier for both datasets was higher than reported previously. For the colorectal cancer dataset, our analysis suggested that GRNs for cancer and normal tissues have a lot of differences, which are most pronounced in the neighborhoods of oncogenes and known cancer tissue markers. The identified differences in gene networks of cancer and normal cells may be used for the discovery of targeted therapies.

Sludge bulking monitoring in industrial wastewater treatment plants through graphical methods: A dynamic graph embedding and Bayesian networks approach.

Sludge bulking is a prevalent issue in wastewater treatment plants (WWTPs) that negatively impacts effluent quality by hindering the normal functioning of treatment processes. To tackle this problem, we propose a novel graph-based monitoring framework that employs advanced graph-based techniques to detect and diagnose sludge bulking events. The proposed framework utilizes historical datasets under normal operating conditions to extract pertinent features and causal relationships between process variables. This enables operators to trigger alarms and diagnose the root cause of the bulking event. Sludge bulking detection is carried out using the dynamic graph embedding (DGE) method, which identifies similarities among process variables in both temporal and neighborhood dependencies. Consequently, the dynamic Bayesian network (DBN) computes the prior and posterior probabilities of a belief, updated at each time step. Variations in these probabilities indicate the potential root cause of the sludge bulking event. The results demonstrate that the DGE outperforms other linear and non-linear feature extraction methods, achieving a detection rate of 99%, zero false alarms, and less than one percent incorrect detections. Additionally, the DBN-based diagnostic method accurately identified the majority of sludge bulking root causes, primarily those resulting from sudden drops in COD concentration, with an accuracy of 98% an improvement of 11% over state-of-the-art techniques.

Dynamic Bayesian networks for stratification of disease progression in amyotrophic lateral sclerosis.

BACKGROUND AND PURPOSE: Progression rate is quite variable in amyotrophic lateral sclerosis (ALS); thus, tools for profiling disease progression are essential for timely interventions. The objective was to apply dynamic Bayesian networks (DBNs) to establish the influence of clinical and demographic variables on disease progression rate. METHODS: In all, 664 ALS patients from our database were included stratified into slow (SP), average (AP) and fast (FP) progressors, according to the Amyotrophic Lateral Sclerosis Functional Rating Scale Revised (ALSFRS-R) rate of decay. The sdtDBN framework was used, a machine learning model which learnt optimal DBNs with both static (gender, age at onset, onset region, body mass index, disease duration at entry, familial history, revised El Escorial criteria and C9orf72) and dynamic (ALSFRS-R scores and sub-scores, forced vital capacity, maximum inspiratory pressure, maximum expiratory pressure and phrenic amplitude) variables. RESULTS: Disease duration and body mass index at diagnosis are the foremost influences amongst static variables. Disease duration is the variable that better discriminates the three groups. Maximum expiratory pressure is the respiratory test with prevalent influence on all groups. ALSFRS score has a higher influence on FP, but lower on AP and SP. The bulbar sub-score has considerable influence on FP but limited on SP. Limb function has a more decisive influence on AP and SP. The respiratory sub-score has little influence in all groups. ALSFRS-R questions 1 (speech) and 9 (climbing stairs) are the most influential in FP and SP, respectively. CONCLUSIONS: The sdtDBN analysis identified five variables, easily obtained during clinical evaluation, which are the most influential for each progression group. This insightful information may help to improve prognosis and care.

Learning dynamic Bayesian networks from time-dependent and time-independent data: Unraveling disease progression in Amyotrophic Lateral Sclerosis.

Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disease causing patients to quickly lose motor neurons. The disease is characterized by a fast functional impairment and ventilatory decline, leading most patients to die from respiratory failure. To estimate when patients should get ventilatory support, it is helpful to adequately profile the disease progression. For this purpose, we use dynamic Bayesian networks (DBNs), a machine learning model, that graphically represents the conditional dependencies among variables. However, the standard DBN framework only includes dynamic (time-dependent) variables, while most ALS datasets have dynamic and static (time-independent) observations. Therefore, we propose the sdtDBN framework, which learns optimal DBNs with static and dynamic variables. Besides learning DBNs from data, with polynomial-time complexity in the number of variables, the proposed framework enables the user to insert prior knowledge and to make inference in the learned DBNs. We use sdtDBNs to study the progression of 1214 patients from a Portuguese ALS dataset. First, we predict the values of every functional indicator in the patients' consultations, achieving results competitive with state-of-the-art studies. Then, we determine the influence of each variable in patients' decline before and after getting ventilatory support. This insightful information can lead clinicians to pay particular attention to specific variables when evaluating the patients, thus improving prognosis. The case study with ALS shows that sdtDBNs are a promising predictive and descriptive tool, which can also be applied to assess the progression of other diseases, given time-dependent and time-independent clinical observations.

A Bayesian Driver Agent Model for Autonomous Vehicles System Based on Knowledge-Aware and Real-Time Data.

A key research area in autonomous driving is how to model the driver's decision-making behavior, due to the fact it is significant for a self-driving vehicles considering their traffic safety and efficiency. However, the uncertain characteristics of vehicle and pedestrian trajectories affect urban roads, which poses severe challenges to the cognitive understanding and decision-making of autonomous vehicle systems in terms of accuracy and robustness. To overcome the abovementioned problems, this paper proposes a Bayesian driver agent (BDA) model which is a vision-based autonomous vehicle system with learning and inference methods inspired by human driver's cognitive psychology. Different from the end-to-end learning method and traditional rule-based methods, our approach breaks the driving system up into a scene recognition module and a decision inference module. The perception module, which is based on a multi-task learning neural network (CNN), takes a driver's-view image as its input and predicts the traffic scene's feature values. The decision module based on dynamic Bayesian network (DBN) then makes an inferred decision using the traffic scene's feature values. To explore the validity of the Bayesian driver agent model, we performed experiments on a driving simulation platform. The BDA model can extract the scene feature values effectively and predict the probability distribution of the human driver's decision-making process accurately based on inference. We take the lane changing scenario as an example to verify the model, the intraclass correlation coefficient (ICC) correlation between the BDA model and human driver's decision process reached 0.984. This work suggests a research in scene perception and autonomous decision-making that may apply to autonomous vehicle system.

Polynomial-Time Algorithm for Learning Optimal BFS-Consistent Dynamic Bayesian Networks.

Dynamic Bayesian networks (DBN) are powerful probabilistic representations that model stochastic processes. They consist of a prior network, representing the distribution over the initial variables, and a set of transition networks, representing the transition distribution between variables over time. It was shown that learning complex transition networks, considering both intra- and inter-slice connections, is NP-hard. Therefore, the community has searched for the largest subclass of DBNs for which there is an efficient learning algorithm. We introduce a new polynomial-time algorithm for learning optimal DBNs consistent with a breadth-first search (BFS) order, named bcDBN. The proposed algorithm considers the set of networks such that each transition network has a bounded in-degree, allowing for p edges from past time slices (inter-slice connections) and k edges from the current time slice (intra-slice connections) consistent with the BFS order induced by the optimal tree-augmented network (tDBN). This approach increases exponentially, in the number of variables, the search space of the state-of-the-art tDBN algorithm. Concerning worst-case time complexity, given a Markov lag m, a set of n random variables ranging over r values, and a set of observations of N individuals over T time steps, the bcDBN algorithm is linear in N, T and m; polynomial in n and r; and exponential in p and k. We assess the bcDBN algorithm on simulated data against tDBN, revealing that it performs well throughout different experiments.

Understanding disease processes by partitioned dynamic Bayesian networks.

For many clinical problems in patients the underlying pathophysiological process changes in the course of time as a result of medical interventions. In model building for such problems, the typical scarcity of data in a clinical setting has been often compensated by utilizing time homogeneous models, such as dynamic Bayesian networks. As a consequence, the specificities of the underlying process are lost in the obtained models. In the current work, we propose the new concept of partitioned dynamic Bayesian networks to capture distribution regime changes, i.e. time non-homogeneity, benefiting from an intuitive and compact representation with the solid theoretical foundation of Bayesian network models. In order to balance specificity and simplicity in real-world scenarios, we propose a heuristic algorithm to search and learn these non-homogeneous models taking into account a preference for less complex models. An extensive set of experiments were ran, in which simulating experiments show that the heuristic algorithm was capable of constructing well-suited solutions, in terms of goodness of fit and statistical distance to the original distributions, in consonance with the underlying processes that generated data, whether it was homogeneous or non-homogeneous. Finally, a study case on psychotic depression was conducted using non-homogeneous models learned by the heuristic, leading to insightful answers for clinically relevant questions concerning the dynamics of this mental disorder.

A dynamic probabilistic model of the onset and interaction of cardio-metabolic comorbidities on an ageing adult population.

Comorbidity is widespread in the ageing population, implying multiple and complex medical needs for individuals and a public health burden. Determining risk factors and predicting comorbidity development can help identify at-risk subjects and design prevention strategies. Using socio-demographic and clinical data from approximately 11,000 subjects monitored over 11 years in the English Longitudinal Study of Ageing, we develop a dynamic Bayesian network (DBN) to model the onset and interaction of three cardio-metabolic comorbidities, namely type 2 diabetes (T2D), hypertension, and heart problems. The DBN allows us to identify risk factors for developing each morbidity, simulate ageing progression over time, and stratify the population based on the risk of outcome occurrence. By applying hierarchical agglomerative clustering to the simulated, dynamic risk of experiencing morbidities, we identified patients with similar risk patterns and the variables contributing to their discrimination. The network reveals a direct joint effect of biomarkers and lifestyle on outcomes over time, such as the impact of fasting glucose, HbA1c, and BMI on T2D development. Mediated cross-relationships between comorbidities also emerge, showcasing the interconnected nature of these health issues. The model presents good calibration and discrimination ability, particularly in predicting the onset of T2D (iAUC-ROC = 0.828, iAUC-PR = 0.294) and survival (iAUC-ROC = 0.827, iAUC-PR = 0.311). Stratification analysis unveils two distinct clusters for all comorbidities, effectively discriminated by variables like HbA1c for T2D and age at baseline for heart problems. The developed DBN constitutes an effective, highly-explainable predictive risk tool for simulating and stratifying the dynamic risk of developing cardio-metabolic comorbidities. Its use could help identify the effects of risk factors and develop health policies that prevent the occurrence of comorbidities.

Dynamic Bayesian network structure learning based on an improved bacterial foraging optimization algorithm.

With the rapid development of artificial intelligence and data science, Dynamic Bayesian Network (DBN), as an effective probabilistic graphical model, has been widely used in many engineering fields. And swarm intelligence algorithm is an optimization algorithm based on natural selection with the characteristics of distributed, self-organization and robustness. By applying the high-performance swarm intelligence algorithm to DBN structure learning, we can fully utilize the algorithm's global search capability to effectively process time-based data, improve the efficiency of network generation and the accuracy of network structure. This study proposes an improved bacterial foraging optimization algorithm (IBFO-A) to solve the problems of random step size, limited group communication, and the inability to maintain a balance between global and local searching. The IBFO-A algorithm framework comprises four layers. First, population initialization is achieved using a logistics-sine chaotic mapping strategy as the basis for global optimization. Second, the activity strategy of a colony foraging trend is constructed by combining the exploration phase of the Osprey optimization algorithm. Subsequently, the strategy of bacterial colony propagation is improved using a "genetic" approach and the Multi-point crossover operator. Finally, the elimination-dispersal activity strategy is employed to escape the local optimal solution. To solve the problem of complex DBN learning structures due to the introduction of time information, a DBN structure learning method called IBFO-D, which is based on the IBFO-A algorithm framework, is proposed. IBFO-D determines the edge direction of the structure by combining the dynamic K2 scoring function, the designed V-structure orientation rule, and the trend activity strategy. Then, according to the improved reproductive activity strategy, the concept of "survival of the fittest" is applied to the network candidate solution while maintaining species diversity. Finally, the global optimal network structure with the highest score is obtained based on the elimination-dispersal activity strategy. Multiple tests and comparison experiments were conducted on 10 sets of benchmark test functions, two non-temporal and temporal data types, and six data samples of two benchmark 2T-BN networks to evaluate and analyze the optimization performance and structure learning ability of the proposed algorithm under various data types. The experimental results demonstrated that IBFO-A exhibits good convergence, stability, and accuracy, whereas IBFO-D is an effective approach for learning DBN structures from data and has practical value for engineering applications.

Improved brain effective connectivity modelling by dynamic Bayesian networks.

BACKGROUND: If brain effective connectivity network modelling (ECN) could be accurately achieved, early diagnosis of neurodegenerative diseases would be possible. It has been observed in the literature that Dynamic Bayesian Network (DBN) based methods are more successful than others. However, DBNs have not been applied easily and tested much due to computational complexity problems in structure learning. NEW METHOD: This study introduces an advanced method for modelling brain ECNs using improved discrete DBN (Improved- dDBN) which addresses the computational challenges previously limiting DBN application, offering solutions that enable accurate and fast structure modelling. RESULTS: The practical data and prior sizes needed for the convergence to the globally correct network structure are proved to be much smaller than the theoretical ones using simulated dDBN data. Besides, Hill Climbing is shown to converge to the true structure at a reasonable iteration step size when the appropriate data and prior sizes are used. Finally, importance of data quantization methods are analysed. COMPARISON WITH EXISTING METHODS: The Improved-dDBN method performs better and robust, when compared to the existing methods for realistic scenarios such as varying graph complexity, various input conditions, noise cases and non-stationary connections. The data used in these tests is the simulated fMRI BOLD time series proposed in the literature. CONCLUSIONS: Improved-dDBN is a good candidate to be used on real datasets to accelerate developments in brain ECN modelling and neuroscience. Appropriate data and prior sizes can be identified based on the approach proposed in this study for global and fast convergence.

Learning the structure of the mTOR protein signaling pathway from protein phosphorylation data.

Statistical learning of the structures of cellular networks, such as protein signaling pathways, is a topical research field in computational systems biology. To get the most information out of experimental data, it is often required to develop a tailored statistical approach rather than applying one of the off-the-shelf network reconstruction methods. The focus of this paper is on learning the structure of the mTOR protein signaling pathway from immunoblotting protein phosphorylation data. Under two experimental conditions eleven phosphorylation sites of eight key proteins of the mTOR pathway were measured at ten non-equidistant time points. For the statistical analysis we propose a new advanced hierarchically coupled non-homogeneous dynamic Bayesian network (NH-DBN) model, and we consider various data imputation methods for dealing with non-equidistant temporal observations. Because of the absence of a true gold standard network, we propose to use predictive probabilities in combination with a leave-one-out cross validation strategy to objectively cross-compare the accuracies of different NH-DBN models and data imputation methods. Finally, we employ the best combination of model and data imputation method for predicting the structure of the mTOR protein signaling pathway.

A Bayesian framework for the automated online assessment of sensor data quality.

Online automated quality assessment is critical to determine a sensor's fitness for purpose in real-time applications. A Dynamic Bayesian Network (DBN) framework is proposed to produce probabilistic quality assessments and represent the uncertainty of sequentially correlated sensor readings. This is a novel framework to represent the causes, quality state and observed effects of individual sensor errors without imposing any constraints upon the physical deployment or measured phenomenon. It represents the casual relationship between quality tests and combines them in a way to generate uncertainty estimates of samples. The DBN was implemented for a particular marine deployment of temperature and conductivity sensors in Hobart, Australia. The DBN was shown to offer a substantial average improvement (34%) in replicating the error bars that were generated by experts when compared to a fuzzy logic approach.

Evidence centered design framework and dynamic bayesian network for modeling learning progression in online assessment system.

An overarching mission of the educational assessment community today is strengthening the connection between assessment and learning. To support this effort, researchers draw variously on developments across technology, analytic methods, assessment design frameworks, research in learning domains, and cognitive, social, and situated psychology. The study lays out the connection among three such developments, namely learning progressions, evidence-centered assessment design (ECD), and dynamic Bayesian modeling for measuring students' advancement along learning progression in a substantive domain. Their conjunction can be applied in both formative and summative assessment uses. In addition, this study conducted an application study in domain of beginning computer network engineering for illustrating the ideas with data drawn from the Cisco Networking Academy's online assessment system.

ICU admission and mortality classifiers for COVID-19 patients based on subgroups of dynamically associated profiles across multiple timepoints.

The coronavirus disease 2019 (COVID-19) which is caused by severe acute respiratory syndrome coronavirus type 2 (SARS-CoV-2) is consistently causing profound wounds in the global healthcare system due to its increased transmissibility. Currently, there is an urgent unmet need to identify the underlying dynamic associations among COVID-19 patients and distinguish patient subgroups with common clinical profiles towards the development of robust classifiers for ICU admission and mortality. To address this need, we propose a four step pipeline which: (i) enhances the quality of multiple timeseries clinical data through an automated data curation workflow, (ii) deploys Dynamic Bayesian Networks (DBNs) for the detection of features with increased connectivity based on dynamic association analysis across multiple points, (iii) utilizes Self Organizing Maps (SOMs) and trajectory analysis for the early identification of COVID-19 patients with common clinical profiles, and (iv) trains robust multiple additive regression trees (MART) for ICU admission and mortality classification based on the extracted homogeneous clusters, to identify risk factors and biomarkers for disease progression. The contribution of the extracted clusters and the dynamically associated clinical data improved the classification performance for ICU admission to sensitivity 0.83 and specificity 0.83, and for mortality to sensitivity 0.74 and specificity 0.76. Additional information was included to enhance the performance of the classifiers yielding an increase by 4% in sensitivity and specificity for mortality. According to the risk factor analysis, the number of lymphocytes, SatO2, PO2/FiO2, and O2 supply type were highlighted as risk factors for ICU admission and the percentage of neutrophils and lymphocytes, PO2/FiO2, LDH, and ALP for mortality, among others. To our knowledge, this is the first study that combines dynamic modeling with clustering analysis to identify homogeneous groups of COVID-19 patients towards the development of robust classifiers for ICU admission and mortality.

Predicting functional impairment trajectories in amyotrophic lateral sclerosis: a probabilistic, multifactorial model of disease progression.

OBJECTIVE: To employ Artificial Intelligence to model, predict and simulate the amyotrophic lateral sclerosis (ALS) progression over time in terms of variable interactions, functional impairments, and survival. METHODS: We employed demographic and clinical variables, including functional scores and the utilisation of support interventions, of 3940 ALS patients from four Italian and two Israeli registers to develop a new approach based on Dynamic Bayesian Networks (DBNs) that models the ALS evolution over time, in two distinct scenarios of variable availability. The method allows to simulate patients' disease trajectories and predict the probability of functional impairment and survival at different time points. RESULTS: DBNs explicitly represent the relationships between the variables and the pathways along which they influence the disease progression. Several notable inter-dependencies were identified and validated by comparison with literature. Moreover, the implemented tool allows the assessment of the effect of different markers on the disease course, reproducing the probabilistically expected clinical progressions. The tool shows high concordance in terms of predicted and real prognosis, assessed as time to functional impairments and survival (integral of the AU-ROC in the first 36 months between 0.80-0.93 and 0.84-0.89 for the two scenarios, respectively). CONCLUSIONS: Provided only with measurements commonly collected during the first visit, our models can predict time to the loss of independence in walking, breathing, swallowing, communicating, and survival and it can be used to generate in silico patient cohorts with specific characteristics. Our tool provides a comprehensive framework to support physicians in treatment planning and clinical decision-making.

Dynamic Bayesian Networks for Integrating Multi-omics Time Series Microbiome Data.

A key challenge in the analysis of longitudinal microbiome data is the inference of temporal interactions between microbial taxa, their genes, the metabolites that they consume and produce, and host genes. To address these challenges, we developed a computational pipeline, a pipeline for the analysis of longitudinal multi-omics data (PALM), that first aligns multi-omics data and then uses dynamic Bayesian networks (DBNs) to reconstruct a unified model. Our approach overcomes differences in sampling and progression rates, utilizes a biologically inspired multi-omic framework, reduces the large number of entities and parameters in the DBNs, and validates the learned network. Applying PALM to data collected from inflammatory bowel disease patients, we show that it accurately identifies known and novel interactions. Targeted experimental validations further support a number of the predicted novel metabolite-taxon interactions.IMPORTANCE While a number of large consortia collect and profile several different types of microbiome and genomic time series data, very few methods exist for joint modeling of multi-omics data sets. We developed a new computational pipeline, PALM, which uses dynamic Bayesian networks (DBNs) and is designed to integrate multi-omics data from longitudinal microbiome studies. When used to integrate sequence, expression, and metabolomics data from microbiome samples along with host expression data, the resulting models identify interactions between taxa, their genes, and the metabolites that they produce and consume, as well as their impact on host expression. We tested the models both by using them to predict future changes in microbiome levels and by comparing the learned interactions to known interactions in the literature. Finally, we performed experimental validations for a few of the predicted interactions to demonstrate the ability of the method to identify novel relationships and their impact.

Cancer classification from time series microarray data through regulatory Dynamic Bayesian Networks.

Genomic profiling of cancer studies has generated comprehensive gene expression patterns for diverse phenotypes. Computational methods which employ transcriptomics datasets have been proposed to model gene expression data. Dynamic Bayesian Networks (DBNs) have been used for modeling time series datasets and for the inference of regulatory networks. Furthermore, cancer classification through DBN-based approaches could reveal the importance of exploiting knowledge from statistically significant genes and key regulatory molecules. Although microarray datasets have been employed extensively by several classification methods for decision making, the use of new knowledge from the pathway level has not been addressed adequately in the literature in terms of DBNs for cancer classification. In the present study, we identify the genes that act as regulators and mediate the activity of transcription factors that have been found in all promoters of our differentially expressed gene sets. These features serve as potential priors for distinguishing tumor from normal samples using a DBN-based classification approach. We employed three microarray datasets from the Gene Expression Omnibus (GEO) public functional repository and performed differential expression analysis. Promoter and pathway analysis of the identified genes revealed the key regulators which influence the transcription mechanisms of these genes. We applied the DBN algorithm on selected genes and identified the features that can accurately classify the samples into tumors and controls. Both accuracy and Area Under the Curve (AUC) were high for the gene sets comprising of the differentially expressed genes along with their master regulators (accuracy: 70.8%-98.5%; AUC: 0.562-0.985).

Statistical Network Inference for Time-Varying Molecular Data with Dynamic Bayesian Networks.

In this chapter, we review the problem of network inference from time-course data, focusing on a class of graphical models known as dynamic Bayesian networks (DBNs). We discuss the relationship of DBNs to models based on ordinary differential equations, and consider extensions to nonlinear time dynamics. We provide an introduction to time-varying DBN models, which allow for changes to the network structure and parameters over time. We also discuss causal perspectives on network inference, including issues around model semantics that can arise due to missing variables. We present a case study of applying time-varying DBNs to gene expression measurements over the life cycle of Drosophila melanogaster. We finish with a discussion of future perspectives, including possible applications of time-varying network inference to single-cell gene expression data.

Restricted-derestricted dynamic Bayesian Network inference of transcriptional regulatory relationships among genes in cancer.

Understanding transcriptional regulatory relationships among genes is important for gaining etiological insights into diseases such as cancer. To this end, high-throughput biological data have been generated through advancements in a variety of technologies. These rely on computational approaches to discover underlying structures in such data. Among these computational approaches, Bayesian networks (BNs) stand out because their probabilistic nature enables them to manage randomness in the dynamics of gene regulation and experimental data. Feedback loops inherent in networks of regulatory relationships are more tractable when enhancements to BNs are applied to them. Here, we propose Restricted-Derestricted dynamic BNs with a novel search technique, Restricted-Derestricted Greedy Method, for such tasks. This approach relies on the Restricted-Derestricted Greedy search technique to infer transcriptional regulatory networks in two phases: restricted inference and derestricted inference. An application of this approach to real data sets reveals it performs favourably well compared to other existing well performing dynamic BN approaches in terms of recovering true relationships among genes. In addition, it provides a balance between searching for optimal networks and keeping biologically relevant regulatory interactions among variables.

Probabilistic model data of time-dependent accident scenarios for a mixing tank mechanical system.

This article presents the risk assessment of a mixing tank mechanical system based on the failure probabilities of the components. Possible component failures can cause accidents which evolve over multiple time stages and can lead to system failure. The consequences of these accident scenarios are analyzed by quantifying the failure probabilities and severity of their outcomes. Illustrative costs and updated failure probabilities are provided to evaluate preventive safety measures. Data refers to the results of the Bayesian model presented in our research article (Mancuso et al., 2019).