Domino Effect Analysis Using Bayesian Networks

A new methodology is introduced based on Bayesian network both to model domino effect propagation patterns and to estimate the domino effect probability at different levels. The flexible structure and the unique modeling techniques offered by Bayesian network make it possible to analyze domino effects through a probabilistic framework, considering synergistic effects, noisy probabilities, and common cause failures. Further, the uncertainties and the complex interactions among the domino effect components are captured using Bayesian network. The probabilities of events are updated in the light of new information, and the most probable path of the domino effect is determined on the basis of the new data gathered. This study shows how probability updating helps to update the domino effect model either qualitatively or quantitatively. The methodology is applied to a hypothetical example and also to an earlier‐studied case study. These examples accentuate the effectiveness of Bayesian network in modeling domino effects in processing facility.     

A Bayesian Network Estimation of the Service‐Profit Chain for Transport Service Satisfaction

Bayesian network methodology is used to model key linkages of the service‐profit chain within the context of transportation service satisfaction. Bayesian networks offer some advantages for implementing managerially focused models over other statistical techniques designed primarily for evaluating theoretical models. These advantages are (1) providing a causal explanation using observable variables within a single multivariate model, (2) analysis of nonlinear relationships contained in ordinal measurements, (3) accommodation of branching patterns that occur in data collection, and (4) the ability to conduct probabilistic inference for prediction and diagnostics with an output metric that can be understood by managers and academics. Sample data from 1,101 recent transport service customers are utilized to select and validate a Bayesian network and conduct probabilistic inference.     

Application of Bayesian Networks in Quantitative Risk Assessment of Subsea Blowout Preventer Operations

This article proposes a methodology for the application of Bayesian networks in conducting quantitative risk assessment of operations in offshore oil and gas industry. The method involves translating a flow chart of operations into the Bayesian network directly. The proposed methodology consists of five steps. First, the flow chart is translated into a Bayesian network. Second, the influencing factors of the network nodes are classified. Third, the Bayesian network for each factor is established. Fourth, the entire Bayesian network model is established. Lastly, the Bayesian network model is analyzed. Subsequently, five categories of influencing factors, namely, human, hardware, software, mechanical, and hydraulic, are modeled and then added to the main Bayesian network. The methodology is demonstrated through the evaluation of a case study that shows the probability of failure on demand in closing subsea ram blowout preventer operations. The results show that mechanical and hydraulic factors have the most important effects on operation safety. Software and hardware factors have almost no influence, whereas human factors are in between. The results of the sensitivity analysis agree with the findings of the quantitative analysis. The three‐axiom‐based analysis partially validates the correctness and rationality of the proposed Bayesian network model.     

Updating Uncertainty in an Integrated Risk Assessment: Conceptual Framework and Methods

Bayesian methods are presented for updating the uncertainty in the predictions of an integrated Environmental Health Risk Assessment (EHRA) model. The methods allow the estimation of posterior uncertainty distributions based on the observation of different model outputs along the chain of the linked assessment framework. Analytical equations are derived for the case of the multiplicative lognormal risk model where the sequential log outputs (log ambient concentration, log applied dose, log delivered dose, and log risk) are each normally distributed. Given observations of a log output made with a normally distributed measurement error, the posterior distributions of the log outputs remain normal, but with modified means and variances, and induced correlations between successive log outputs and log inputs. The analytical equations for forward and backward propagation of the updates are generally applicable to sums of normally distributed variables. The Bayesian Monte-Carlo (BMC) procedure is presented to provide an approximate, but more broadly applicable method for numerically updating uncertainty with concurrent backward and forward propagation. Illustrative examples, presented for the multiplicative lognormal model, demonstrate agreement between the analytical and BMC methods, and show how uncertainty updates can propagate through a linked EHRA. The Bayesian updating methods facilitate the pooling of knowledge encoded in predictive models with that transmitted by research outcomes (e.g., field measurements), and thereby support the practice of iterative risk assessment and value of information appraisals.     

Campylobacter QMRA: A Bayesian Estimation of Prevalence and Concentration in Retail Foods Under Clustering and Heavy Censoring

A Bayesian statistical temporal‐prevalence‐concentration model (TPCM) was built to assess the prevalence and concentration of pathogenic campylobacter species in batches of fresh chicken and turkey meat at retail. The data set was collected from Finnish grocery stores in all the seasons of the year. Observations at low concentration levels are often censored due to the limit of determination of the microbiological methods. This model utilized the potential of Bayesian methods to borrow strength from related samples in order to perform under heavy censoring. In this extreme case the majority of the observed batch‐specific concentrations was below the limit of determination. The hierarchical structure was included in the model in order to take into account the within‐batch and between‐batch variability, which may have a significant impact on the sample outcome depending on the sampling plan. Temporal changes in the prevalence of campylobacter were modeled using a Markovian time series. The proposed model is adaptable for other pathogens if the same type of data set is available. The computation of the model was performed using OpenBUGS software.     

Inferring an Augmented Bayesian Network to Confront a Complex Quantitative Microbial Risk Assessment Model with Durability Studies: Application to Bacillus Cereus on a Courgette Purée Production Chain

The Monte Carlo (MC) simulation approach is traditionally used in food safety risk assessment to study quantitative microbial risk assessment (QMRA) models. When experimental data are available, performing Bayesian inference is a good alternative approach that allows backward calculation in a stochastic QMRA model to update the experts’ knowledge about the microbial dynamics of a given food‐borne pathogen. In this article, we propose a complex example where Bayesian inference is applied to a high‐dimensional second‐order QMRA model. The case study is a farm‐to‐fork QMRA model considering genetic diversity of Bacillus cereus in a cooked, pasteurized, and chilled courgette purée. Experimental data are Bacillus cereus concentrations measured in packages of courgette purées stored at different time‐temperature profiles after pasteurization. To perform a Bayesian inference, we first built an augmented Bayesian network by linking a second‐order QMRA model to the available contamination data. We then ran a Markov chain Monte Carlo (MCMC) algorithm to update all the unknown concentrations and unknown quantities of the augmented model. About 25% of the prior beliefs are strongly updated, leading to a reduction in uncertainty. Some updates interestingly question the QMRA model.     

Sign Restrictions,Structural Vector Autoregressions,and Useful Prior Information

This paper makes the following original contributions to the literature. (i) We develop a simpler analytical characterization and numerical algorithm for Bayesian inference in structural vector autoregressions (VARs) that can be used for models that are overidentified, just‐identified, or underidentified. (ii) We analyze the asymptotic properties of Bayesian inference and show that in the underidentified case, the asymptotic posterior distribution of contemporaneous coefficients in an n‐variable VAR is confined to the set of values that orthogonalize the population variance–covariance matrix of ordinary least squares residuals, with the height of the posterior proportional to the height of the prior at any point within that set. For example, in a bivariate VAR for supply and demand identified solely by sign restrictions, if the population correlation between the VAR residuals is positive, then even if one has available an infinite sample of data, any inference about the demand elasticity is coming exclusively from the prior distribution. (iii) We provide analytical characterizations of the informative prior distributions for impulse‐response functions that are implicit in the traditional sign‐restriction approach to VARs, and we note, as a special case of result (ii), that the influence of these priors does not vanish asymptotically. (iv) We illustrate how Bayesian inference with informative priors can be both a strict generalization and an unambiguous improvement over frequentist inference in just‐identified models. (v) We propose that researchers need to explicitly acknowledge and defend the role of prior beliefs in influencing structural conclusions and we illustrate how this could be done using a simple model of the U.S. labor market.     

Nonparametric Estimation of the Probability of Detection of Flaws in an Industrial Component,from Destructive and Nondestructive Testing Data,Using Approximate Bayesian Computation

We consider the problem of estimating the probability of detection (POD) of flaws in an industrial steel component. Modeled as an increasing function of the flaw height, the POD characterizes the detection process; it is also involved in the estimation of the flaw size distribution, a key input parameter of physical models describing the behavior of the steel component when submitted to extreme thermodynamic loads. Such models are used to assess the resistance of highly reliable systems whose failures are seldom observed in practice. We develop a Bayesian method to estimate the flaw size distribution and the POD function, using flaw height measures from periodic in‐service inspections conducted with an ultrasonic detection device, together with measures from destructive lab experiments. Our approach, based on approximate Bayesian computation (ABC) techniques, is applied to a real data set and compared to maximum likelihood estimation (MLE) and a more classical approach based on Markov Chain Monte Carlo (MCMC) techniques. In particular, we show that the parametric model describing the POD as the cumulative distribution function (cdf) of a log‐normal distribution, though often used in this context, can be invalidated by the data at hand. We propose an alternative nonparametric model, which assumes no predefined shape, and extend the ABC framework to this setting. Experimental results demonstrate the ability of this method to provide a flexible estimation of the POD function and describe its uncertainty accurately.     

A Three‐Part Bayesian Network for Modeling Dwelling Fires and Their Impact upon People and Property

In the United Kingdom, dwelling fires are responsible for the majority of all fire‐related fatalities. The development of these incidents involves the interaction of a multitude of variables that combine in many different ways. Consequently, assessment of dwelling fire risk can be complex, which often results in ambiguity during fire safety planning and decision making. In this article, a three‐part Bayesian network model is proposed to study dwelling fires from ignition through to extinguishment in order to improve confidence in dwelling fire safety assessment. The model incorporates both hard and soft data, delivering posterior probabilities for selected outcomes. Case studies demonstrate how the model functions and provide evidence of its use for planning and accident investigation.     

Harnessing the Theoretical Foundations of the Exponential and Beta‐Poisson Dose‐Response Models to Quantify Parameter Uncertainty Using Markov Chain Monte Carlo

Dose‐response models are the essential link between exposure assessment and computed risk values in quantitative microbial risk assessment, yet the uncertainty that is inherent to computed risks because the dose‐response model parameters are estimated using limited epidemiological data is rarely quantified. Second‐order risk characterization approaches incorporating uncertainty in dose‐response model parameters can provide more complete information to decisionmakers by separating variability and uncertainty to quantify the uncertainty in computed risks. Therefore, the objective of this work is to develop procedures to sample from posterior distributions describing uncertainty in the parameters of exponential and beta‐Poisson dose‐response models using Bayes's theorem and Markov Chain Monte Carlo (in OpenBUGS). The theoretical origins of the beta‐Poisson dose‐response model are used to identify a decomposed version of the model that enables Bayesian analysis without the need to evaluate Kummer confluent hypergeometric functions. Herein, it is also established that the beta distribution in the beta‐Poisson dose‐response model cannot address variation among individual pathogens, criteria to validate use of the conventional approximation to the beta‐Poisson model are proposed, and simple algorithms to evaluate actual beta‐Poisson probabilities of infection are investigated. The developed MCMC procedures are applied to analysis of a case study data set, and it is demonstrated that an important region of the posterior distribution of the beta‐Poisson dose‐response model parameters is attributable to the absence of low‐dose data. This region includes beta‐Poisson models for which the conventional approximation is especially invalid and in which many beta distributions have an extreme shape with questionable plausibility.     

A gradient Markov chain Monte Carlo algorithm for computing multivariate maximum likelihood estimates and posterior distributions: mixture dose-response assessment

Multivariate probability distributions, such as may be used for mixture dose‐response assessment, are typically highly parameterized and difficult to fit to available data. However, such distributions may be useful in analyzing the large electronic data sets becoming available, such as dose‐response biomarker and genetic information. In this article, a new two‐stage computational approach is introduced for estimating multivariate distributions and addressing parameter uncertainty. The proposed first stage comprises a gradient Markov chain Monte Carlo (GMCMC) technique to find Bayesian posterior mode estimates (PMEs) of parameters, equivalent to maximum likelihood estimates (MLEs) in the absence of subjective information. In the second stage, these estimates are used to initialize a Markov chain Monte Carlo (MCMC) simulation, replacing the conventional burn‐in period to allow convergent simulation of the full joint Bayesian posterior distribution and the corresponding unconditional multivariate distribution (not conditional on uncertain parameter values). When the distribution of parameter uncertainty is such a Bayesian posterior, the unconditional distribution is termed predictive. The method is demonstrated by finding conditional and unconditional versions of the recently proposed emergent dose‐response function (DRF). Results are shown for the five‐parameter common‐mode and seven‐parameter dissimilar‐mode models, based on published data for eight benzene–toluene dose pairs. The common mode conditional DRF is obtained with a 21‐fold reduction in data requirement versus MCMC. Example common‐mode unconditional DRFs are then found using synthetic data, showing a 71% reduction in required data. The approach is further demonstrated for a PCB 126‐PCB 153 mixture. Applicability is analyzed and discussed. Matlab^® computer programs are provided.     

Use of Markov Chain Monte Carlo Analysis with a Physiologically-Based Pharmacokinetic Model of Methylmercury to Estimate Exposures in U.S. Women of Childbearing Age

A Bayesian approach, implemented using Markov Chain Monte Carlo (MCMC) analysis, was applied with a physiologically‐based pharmacokinetic (PBPK) model of methylmercury (MeHg) to evaluate the variability of MeHg exposure in women of childbearing age in the U.S. population. The analysis made use of the newly available National Health and Nutrition Survey (NHANES) blood and hair mercury concentration data for women of age 16–49 years (sample size, 1,582). Bayesian analysis was performed to estimate the population variability in MeHg exposure (daily ingestion rate) implied by the variation in blood and hair concentrations of mercury in the NHANES database. The measured variability in the NHANES blood and hair data represents the result of a process that includes interindividual variation in exposure to MeHg and interindividual variation in the pharmacokinetics (distribution, clearance) of MeHg. The PBPK model includes a number of pharmacokinetic parameters (e.g., tissue volumes, partition coefficients, rate constants for metabolism and elimination) that can vary from individual to individual within the subpopulation of interest. Using MCMC analysis, it was possible to combine prior distributions of the PBPK model parameters with the NHANES blood and hair data, as well as with kinetic data from controlled human exposures to MeHg, to derive posterior distributions that refine the estimates of both the population exposure distribution and the pharmacokinetic parameters. In general, based on the populations surveyed by NHANES, the results of the MCMC analysis indicate that a small fraction, less than 1%, of the U.S. population of women of childbearing age may have mercury exposures greater than the EPA RfD for MeHg of 0.1 μg/kgg/day, and that there are few, if any, exposures greater than the ATSDR MRL of 0.3 μgg/kgg/day. The analysis also indicates that typical exposures may be greater than previously estimated from food consumption surveys, but that the variability in exposure within the population of U.S. women of childbearing age may be less than previously assumed.     

Using Bayesian Networks to Model Expected and Unexpected Operational Losses

This report describes the use of Bayesian networks (BNs) to model statistical loss distributions in financial operational risk scenarios. Its focus is on modeling "long" tail, or unexpected, loss events using mixtures of appropriate loss frequency and severity distributions where these mixtures are conditioned on causal variables that model the capability or effectiveness of the underlying controls process. The use of causal modeling is discussed from the perspective of exploiting local expertise about process reliability and formally connecting this knowledge to actual or hypothetical statistical phenomena resulting from the process. This brings the benefit of supplementing sparse data with expert judgment and transforming qualitative knowledge about the process into quantitative predictions. We conclude that BNs can help combine qualitative data from experts and quantitative data from historical loss databases in a principled way and as such they go some way in meeting the requirements of the draft Basel II Accord (Basel, 2004) for an advanced measurement approach (AMA).     

Methods for Assessing Uncertainty in Fundamental Assumptions and Associated Models for Cancer Risk Assessment

The distributional approach for uncertainty analysis in cancer risk assessment is reviewed and extended. The method considers a combination of bioassay study results, targeted experiments, and expert judgment regarding biological mechanisms to predict a probability distribution for uncertain cancer risks. Probabilities are assigned to alternative model components, including the determination of human carcinogenicity, mode of action, the dosimetry measure for exposure, the mathematical form of the dose‐response relationship, the experimental data set(s) used to fit the relationship, and the formula used for interspecies extrapolation. Alternative software platforms for implementing the method are considered, including Bayesian belief networks (BBNs) that facilitate assignment of prior probabilities, specification of relationships among model components, and identification of all output nodes on the probability tree. The method is demonstrated using the application of Evans, Sielken, and co‐workers for predicting cancer risk from formaldehyde inhalation exposure. Uncertainty distributions are derived for maximum likelihood estimate (MLE) and 95th percentile upper confidence limit (UCL) unit cancer risk estimates, and the effects of resolving selected model uncertainties on these distributions are demonstrated, considering both perfect and partial information for these model components. A method for synthesizing the results of multiple mechanistic studies is introduced, considering the assessed sensitivities and selectivities of the studies for their targeted effects. A highly simplified example is presented illustrating assessment of genotoxicity based on studies of DNA damage response caused by naphthalene and its metabolites. The approach can provide a formal mechanism for synthesizing multiple sources of information using a transparent and replicable weight‐of‐evidence procedure.     

Estimation of a Benchmark Dose in the Presence or Absence of Hormesis Using Posterior Averaging

U.S. Environment Protection Agency benchmark doses for dichotomous cancer responses are often estimated using a multistage model based on a monotonic dose‐response assumption. To account for model uncertainty in the estimation process, several model averaging methods have been proposed for risk assessment. In this article, we extend the usual parameter space in the multistage model for monotonicity to allow for the possibility of a hormetic dose‐response relationship. Bayesian model averaging is used to estimate the benchmark dose and to provide posterior probabilities for monotonicity versus hormesis. Simulation studies show that the newly proposed method provides robust point and interval estimation of a benchmark dose in the presence or absence of hormesis. We also apply the method to two data sets on carcinogenic response of rats to 2,3,7,8‐tetrachlorodibenzo‐p‐dioxin.     

Bayesian Inference for Reliability of Systems and Networks Using the Survival Signature

The concept of survival signature has recently been introduced as an alternative to the signature for reliability quantification of systems. While these two concepts are closely related for systems consisting of a single type of component, the survival signature is also suitable for systems with multiple types of component, which is not the case for the signature. This also enables the use of the survival signature for reliability of networks. In this article, we present the use of the survival signature for reliability quantification of systems and networks from a Bayesian perspective. We assume that data are available on tested components that are exchangeable with those in the actual system or network of interest. These data consist of failure times and possibly right‐censoring times. We present both a nonparametric and parametric approach.     

Quantal Risk Assessment Database: A Database for Exploring Patterns in Quantal Dose‐Response Data in Risk Assessment and its Application to Develop Priors for Bayesian Dose‐Response Analysis

Quantitative risk assessments for physical, chemical, biological, occupational, or environmental agents rely on scientific studies to support their conclusions. These studies often include relatively few observations, and, as a result, models used to characterize the risk may include large amounts of uncertainty. The motivation, development, and assessment of new methods for risk assessment is facilitated by the availability of a set of experimental studies that span a range of dose‐response patterns that are observed in practice. We describe construction of such a historical database focusing on quantal data in chemical risk assessment, and we employ this database to develop priors in Bayesian analyses. The database is assembled from a variety of existing toxicological data sources and contains 733 separate quantal dose‐response data sets. As an illustration of the database's use, prior distributions for individual model parameters in Bayesian dose‐response analysis are constructed. Results indicate that including prior information based on curated historical data in quantitative risk assessments may help stabilize eventual point estimates, producing dose‐response functions that are more stable and precisely estimated. These in turn produce potency estimates that share the same benefit. We are confident that quantitative risk analysts will find many other applications and issues to explore using this database.     

Bayesian Methods for Model Uncertainty Analysis with Application to Future Sea Level Rise

This paper addresses the use of data for identifying and characterizing uncertainties in model parameters and predictions. The Bayesian Monte Carlo method is formally presented and elaborated, and applied to the analysis of the uncertainty in a predictive model for global mean sea level change. The method uses observations of output variables, made with an assumed error structure, to determine a posterior distribution of model outputs. This is used to derive a posterior distribution for the model parameters. Results demonstrate the resolution of the uncertainty that is obtained as a result of the Bayesian analysis and also indicate the key contributors to the uncertainty in the sea level rise model. While the technique is illustrated with a simple, preliminary model, the analysis provides an iterative framework for model refinement. The methodology developed in this paper provides a mechanism for the incorporation of ongoing data collection and research in decision-making for problems involving uncertain environmental change.     

基于贝叶斯网络的并发型突发事件链建模方法

现实情形中，由于致灾因子和作用对象的相似性，初始突发事件的发生易引发多个次生事件并发及耦合，致使事件的演化发展及可能造成的损失具有更大的不确定性。然而，现有的突发事件链式演化分析多运用串发型事件链，对于并发型突发事件存在适用性较低的问题。针对上述问题，本文将突发事件抽象描述为以输入、状态和输出属性为组成要素，通过属性要素间的作用关系构成的复杂系统，进而从属性层面分析事件间的关联关系；以贝叶斯网络为建模工具，识别并发型突发事件间具有的因果关系和耦合关系，给出事件贝叶斯网络关联方法，构建并发型突发事件链模型；基于历史数据获取网络节点间的先验概率信息，运用贝叶斯网络推理算法实现并发型突发事件的演化分析；最后，通过实例验证本文方法在实际应用中的科学性及可行性，并通过对比分析阐明其在提高灾害损失预测精度方面具有一定的优势。