Major Accidents (Gray Swans) Likelihood Modeling Using Accident Precursors and Approximate Reasoning

Compared to the remarkable progress in risk analysis of normal accidents, the risk analysis of major accidents has not been so well‐established, partly due to the complexity of such accidents and partly due to low probabilities involved. The issue of low probabilities normally arises from the scarcity of major accidents’ relevant data since such accidents are few and far between. In this work, knowing that major accidents are frequently preceded by accident precursors, a novel precursor‐based methodology has been developed for likelihood modeling of major accidents in critical infrastructures based on a unique combination of accident precursor data, information theory, and approximate reasoning. For this purpose, we have introduced an innovative application of information analysis to identify the most informative near accident of a major accident. The observed data of the near accident were then used to establish predictive scenarios to foresee the occurrence of the major accident. We verified the methodology using offshore blowouts in the Gulf of Mexico, and then demonstrated its application to dam breaches in the United Sates.     

基于HHM-RFRM的船舶航行风险评估方法研究

船舶航行风险是由各种风险因素交互作用产生。综合 HHM-RFRM 理论，构建船舶航行多维风险情景危险度测度模型，以风险因素耦合视角探讨船舶航行风险管理问题。在船舶航行多维风险情景危险度测度模型中结合贝叶斯定理，对船舶航行风险情景进行了定性与定量化过滤、评级。最后以大连港某从事商务活动的货船为例，验证了所提出方法的可行性。传统的风险评估方法只能评估单个风险因素对系统的影响，此评估方法克服了这一局限性，为船舶航行风险管理提供新的视角。     

Estimation and Properties of a Time-Varying EGARCH(1,1) in Mean Model

Time-varying GARCH-M models are commonly employed in econometrics and financial economics. Yet the recursive nature of the conditional variance makes likelihood analysis of these models computationally infeasible. This article outlines the issues and suggests to employ a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a simulated Bayesian solution in only O(T) computational operations, where T is the sample size. Furthermore, the theoretical dynamic properties of a time-varying-parameter EGARCH(1,1)-M are derived. We discuss them and apply the suggested Bayesian estimation to three major stock markets.     

Bayesian estimation of reliability using time-to-failure distribution of parametric degradation models

This paper focusses on computing the Bayesian reliability of components whose performance characteristics (degradation – fatigue and cracks) are observed during a specified period of time. Depending upon the nature of degradation data collected, we fit a monotone increasing or decreasing function for the data. Since the components are supposed to have different lifetimes, the rate of degradation is assumed to be a random variable. At a critical level of degradation, the time to failure distribution is obtained. The exponential and power degradation models are studied and exponential density function is assumed for the random variable representing the rate of degradation. The maximum likelihood estimator and Bayesian estimator of the parameter of exponential density function, predictive distribution, hierarchical Bayes approach and robustness of the posterior mean are presented. The Gibbs sampling algorithm is used to obtain the Bayesian estimates of the parameter. Illustrations are provided for the train wheel degradation data.     

Bayesian blinded sample size re-estimation

Information before unblinding regarding the success of confirmatory clinical trials is highly uncertain. Current techniques using point estimates of auxiliary parameters for estimating expected blinded sample size: (i) fail to describe the range of likely sample sizes obtained after the anticipated data are observed, and (ii) fail to adjust to the changing patient population. Sequential MCMC-based algorithms are implemented for purposes of sample size adjustments. The uncertainty arising from clinical trials is characterized by filtering later auxiliary parameters through their earlier counterparts and employing posterior distributions to estimate sample size and power. The use of approximate expected power estimates to determine the required additional sample size are closely related to techniques employing Simple Adjustments or the EM algorithm. By contrast with these, our proposed methodology provides intervals for the expected sample size using the posterior distribution of auxiliary parameters. Future decisions about additional subjects are better informed due to our ability to account for subject response heterogeneity over time. We apply the proposed methodologies to a depression trial. Our proposed blinded procedures should be considered for most studies due to ease of implementation.     

Robust Bayesian nonlinear mixed‐effects modeling of time to positivity in tuberculosis trials

Early phase 2 tuberculosis (TB) trials are conducted to characterize the early bactericidal activity (EBA) of anti‐TB drugs. The EBA of anti‐TB drugs has conventionally been calculated as the rate of decline in colony forming unit (CFU) count during the first 14 days of treatment. The measurement of CFU count, however, is expensive and prone to contamination. Alternatively to CFU count, time to positivity (TTP), which is a potential biomarker for long‐term efficacy of anti‐TB drugs, can be used to characterize EBA. The current Bayesian nonlinear mixed‐effects (NLME) regression model for TTP data, however, lacks robustness to gross outliers that often are present in the data. The conventional way of handling such outliers involves their identification by visual inspection and subsequent exclusion from the analysis. However, this process can be questioned because of its subjective nature. For this reason, we fitted robust versions of the Bayesian nonlinear mixed‐effects regression model to a wide range of TTP datasets. The performance of the explored models was assessed through model comparison statistics and a simulation study. We conclude that fitting a robust model to TTP data obviates the need for explicit identification and subsequent “deletion” of outliers but ensures that gross outliers exert no undue influence on model fits. We recommend that the current practice of fitting conventional normal theory models be abandoned in favor of fitting robust models to TTP data.     

Mixtures of Gaussian copula factor analyzers for clustering high dimensional data

Mixtures of factor analyzers is a useful model-based clustering method which can avoid the curse of dimensionality in high-dimensional clustering. However, this approach is sensitive to both diverse non-normalities of marginal variables and outliers, which are commonly observed in multivariate experiments. We propose mixtures of Gaussian copula factor analyzers (MGCFA) for clustering high-dimensional clustering. This model has two advantages; (1) it allows different marginal distributions to facilitate fitting flexibility of the mixture model, (2) it can avoid the curse of dimensionality by embedding the factor-analytic structure in the component-correlation matrices of the mixture distribution.An EM algorithm is developed for the fitting of MGCFA. The proposed method is free of the curse of dimensionality and allows any parametric marginal distribution which fits best to the data. It is applied to both synthetic data and a microarray gene expression data for clustering and shows its better performance over several existing methods.     

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.     

Truncation invariant copulas and a testing procedure

ABSTRACT

The class of bivariate copulas that are invariant under truncation with respect to one variable is considered. A simulation algorithm for the members of the class and a novel construction method are presented. Moreover, inspired by a stochastic interpretation of the members of such a class, a procedure is suggested to check whether the dependence structure of a given data set is truncation invariant. The overall performance of the procedure has been illustrated on both simulated and real data.     

Bayesian penalized B-spline estimation approach for epidemic models

Ordinary differential equations (ODEs) are normally used to model dynamic processes in applied sciences such as biology, engineering, physics, and many other areas. In these models, the parameters are usually unknown, and thus they are often specified artificially or empirically. Alternatively, a feasible method is to estimate the parameters based on observed data. In this study, we propose a Bayesian penalized B-spline approach to estimate the parameters and initial values for ODEs used in epidemiology. We evaluated the efficiency of the proposed method based on simulations using the Markov chain Monte Carlo algorithm for the Kermack–McKendrick model. The proposed approach is also illustrated based on a real application to the transmission dynamics of hepatitis C virus in mainland China.