Application of the Hyper‐Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes

The hyper‐Poisson distribution can handle both over‐ and underdispersion, and its generalized linear model formulation allows the dispersion of the distribution to be observation‐specific and dependent on model covariates. This study's objective is to examine the potential applicability of a newly proposed generalized linear model framework for the hyper‐Poisson distribution in analyzing motor vehicle crash count data. The hyper‐Poisson generalized linear model was first fitted to intersection crash data from Toronto, characterized by overdispersion, and then to crash data from railway‐highway crossings in Korea, characterized by underdispersion. The results of this study are promising. When fitted to the Toronto data set, the goodness‐of‐fit measures indicated that the hyper‐Poisson model with a variable dispersion parameter provided a statistical fit as good as the traditional negative binomial model. The hyper‐Poisson model was also successful in handling the underdispersed data from Korea; the model performed as well as the gamma probability model and the Conway‐Maxwell‐Poisson model previously developed for the same data set. The advantages of the hyper‐Poisson model studied in this article are noteworthy. Unlike the negative binomial model, which has difficulties in handling underdispersed data, the hyper‐Poisson model can handle both over‐ and underdispersed crash data. Although not a major issue for the Conway‐Maxwell‐Poisson model, the effect of each variable on the expected mean of crashes is easily interpretable in the case of this new model.     

非定向流量限定型军事路网隐蔽性熵测度及其运输分配研究

考虑到战争时期军需物资运输不存在道路定向的限制,而存在运量有限的要求,本文在已有研究基础上提出了流量限定且隐蔽性最大条件下的非定向军事路网隐蔽性熵测度方法,以及该测度方法下的军需物资运输分配模型。新的隐蔽性测度公式与物资运输分配模型能兼顾非定向性和流量限定两方面约束,更为符合实际需要。此外,文中还分析了非定向和流量限定条件下军事路网多方面性质,即非负性、对称性、扩展性、收发路段的定向性、路网的可转换性以及路网循环流的可能性。结合隐蔽性熵测度方法和路网性质,笔者构建了非定向流量限定条件下军需物资运输分配模型。最后,通过具体算例充分验证了新隐蔽性熵测度方法和运输分配模型的可行性与有效性。     

基于量子二项式模型的实物期权估值算法

研究分析二项式期权定价模型,发现陈泽乾的量子模型新公式与经典CRR公式是互补存在的,有着各自不同的适用范围;进而提出基于量子二项式模型的实物期权估值算法,该算法有机地结合了量子模型新公式和经典CRR公式;最后给出了一个数值示例。     

Estimation from Zero-Failure Data

When performing quantitative (or probabilistic) risk assessments, it is often the case that data for many of the potential events in question are sparse or nonexistent. Some of these events may be well-represented by the binomial probability distribution. In this paper, a model for predicting the binomial failure probability, P , from data that include no failures is examined. A review of the literature indicates that the use of this model is currently limited to risk analysis of energetic initiation in the explosives testing field. The basis for the model is discussed, and the behavior of the model relative to other models developed for the same purpose is investigated. It is found that the qualitative behavior of the model is very similar to that of the other models, and for larger values of n (the number of trials), the predicted P values varied by a factor of about eight among the five models examined. Analysis revealed that the estimator is nearly identical to the median of a Bayesian posterior distribution, derived using a uniform prior. An explanation of the application of the estimator in explosives testing is provided, and comments are offered regarding the use of the estimator versus other possible techniques.     

On the Use of Hierarchical Probabilistic Models for Characterizing and Managing Uncertainty in Risk/Safety Assessment

A general probabilistically-based approach is proposed for both cancer and noncancer risk/safety assessments. The familiar framework of the original ADI/RfD formulation is used, substituting in the numerator a benchmark dose derived from a hierarchical pharmacokinetic/pharmacodynamic model and in the denominator a unitary uncertainty factor derived from a hierarchical animal/average human/sensitive human model. The empirical probability distributions of the numerator and denominator can be combined to produce an empirical human-equivalent distribution for an animal-derived benchmark dose in external-exposure units.     

Improved Methods for Estimating Flood Depth Exceedances Within Storm Surge Protection Systems

Contemporary studies conducted by the U.S. Army Corps of Engineers estimate probability distributions of flooding on the interior of ring levee systems by estimating surge exceedances at points along levee system boundaries, calculating overtopping volumes generated by this surface, then passing the resulting volumes of water through a drainage model to calculate interior flood depths. This approach may not accurately represent the exceedance probability of flood depths within the system interior; a storm producing 100‐year surge at one point is unlikely to simultaneously produce 100‐year surge levels everywhere around the system exterior. A conceptually preferred approach estimates surge and waves associated with a large set of storms. Each storm is run through the interior model separately, and the resulting flood depths are weighted by a parameterized likelihood of each synthetic storm. This results in an empirical distribution of flood depths accounting for geospatial variation in any individual storm's characteristics. This method can also better account for the probability of levee breaches or other system failures. The two methods can produce different estimates of flood depth exceedances and damage when applied to storm surge flooding in coastal Louisiana. Even differences in flood depth exceedances of less than 0.2 m can still produce large differences in projected damage. This article identifies and discusses differences in estimated flood depths and damage produced by each method within multiple Louisiana protection systems. The novel coupled dynamics approach represents a step toward enabling risk‐based design standards.     

Towards a Fuzzy Bayesian Network Based Approach for Safety Risk Analysis of Tunnel‐Induced Pipeline Damage

Tunneling excavation is bound to produce significant disturbances to surrounding environments, and the tunnel‐induced damage to adjacent underground buried pipelines is of considerable importance for geotechnical practice. A fuzzy Bayesian networks (FBNs) based approach for safety risk analysis is developed in this article with detailed step‐by‐step procedures, consisting of risk mechanism analysis, the FBN model establishment, fuzzification, FBN‐based inference, defuzzification, and decision making. In accordance with the failure mechanism analysis, a tunnel‐induced pipeline damage model is proposed to reveal the cause‐effect relationships between the pipeline damage and its influential variables. In terms of the fuzzification process, an expert confidence indicator is proposed to reveal the reliability of the data when determining the fuzzy probability of occurrence of basic events, with both the judgment ability level and the subjectivity reliability level taken into account. By means of the fuzzy Bayesian inference, the approach proposed in this article is capable of calculating the probability distribution of potential safety risks and identifying the most likely potential causes of accidents under both prior knowledge and given evidence circumstances. A case concerning the safety analysis of underground buried pipelines adjacent to the construction of the Wuhan Yangtze River Tunnel is presented. The results demonstrate the feasibility of the proposed FBN approach and its application potential. The proposed approach can be used as a decision tool to provide support for safety assurance and management in tunnel construction, and thus increase the likelihood of a successful project in a complex project environment.     

Improving the resilience of power grids against typhoons with data-driven spatial distributionally robust optimization

In recent years, the increased frequency of natural hazards has led to more disruptions in power grids, potentially causing severe infrastructural damages and cascading failures. Therefore, it is important that the power system resilience be improved by implementing new technology and utilizing optimization methods. This paper proposes a data-driven spatial distributionally robust optimization (DS-DRO) model to provide an optimal plan to install and dispatch distributed energy resources (DERs) against the uncertain impact of natural hazards such as typhoons. We adopt an accurate spatial model to evaluate the failure probability with regard to system components based on wind speed. We construct a moment-based ambiguity set of the failure distribution based on historical typhoon data. A two-stage DS-DRO model is then formulated to obtain an optimal resilience enhancement strategy. We employ the combination of dual reformulation and a column-and-constraints generation algorithm, and showcase the effectiveness of the proposed approach with a modified IEEE 13-node reliability test system projected in the Hong Kong region.     

活动重叠模式与资源约束下的项目调度优化

采取活动重叠模式通常是加速研发的有效手段,带有活动重叠的资源受限项目调度问题是经典资源受限项目调度问题的扩展.首先,深入分析了活动重叠对于项目调度的影响,对活动重叠及其不确定进行详细描述与建模,提出了活动重叠导致下游活动返工时间的二项分布概率模型;其次,构建了以最小化研发项目期望工期为目标的优化调度模型,设计了基于串行进度生成机制的遗传算法对大规模问题进行优化求解;最后,基于PSPLIB J60问题库中480个算例分析了该算法的计算结果,并考察了网络参数、资源参数和重叠参数变化时,采用活动重叠模式对缩短项目工期的影响.研究结果表明:活动对资源的需求强度越小或资源稀缺程度越低,可重叠活动对数量就会增加,项目工期缩短得越明显;网络复杂度的变化对缩短项目工期的影响不大;项目中重叠活动对越多,重叠导致的下游活动返工的概率越小,项目工期缩短的越明显.     

On Criteria of Insignificant Difference Between Two Risks

The comparison and ranking of risks is very important for safety and cost-benefit analysis. Most formats present risks in the form of probability distribution. Different ranking criteria for probability distributions are considered. It is demonstrated that significantly overlapping distributions lead to ambiguous results. For this reason, criteria of insignificant overlapping distributions are proposed. The first criterion uses the information theory approach; and the second criterion uses the statistical tests approach. Both approaches can be applied to decision theory to avoid questionable decisions based on statistically insignificant differences between two risks.     

A Quantitative Risk Assessment of Waterborne Cryptosporidiosis in France Using Second-Order Monte Carlo Simulation

A pragmatic quantitative risk assessment (QRA) of the risks of waterborne Cryptosporidium parvum infection and cryptosporidiosis in immunocompetent and immunodeficient French populations is proposed. The model takes into account French specificities such as the French technique for oocyst enumeration performance and tap water consumption. The proportion of infective oocysts is based on literature review and expert knowledge. The probability of infection for a given number of ingested viable oocysts is modeled using the exponential dose-response model applied on published data from experimental infections in immunocompetent human volunteers challenged with the IOWA strain. Second-order Monte Carlo simulations are used to characterize the uncertainty and variability of the risk estimates. Daily risk of infection and illness for the immunocompetent and the immunodeficient populations are estimated according to the number of oocysts observed in a single storage reservoir water sample. As an example, the mean daily risk of infection in the immunocompetent population is estimated to be 1.08 x 10(-4) (95% confidence interval: [0.20 x 10(-4); 6.83 x 10(-4)]) when five oocysts are observed in a 100 L storage reservoir water sample. Annual risks of infection and disease are estimated from a set of oocyst enumeration results from distributed water samples, assuming a negative binomial distribution of day-to-day contamination variation. The model and various assumptions used in the model are fully explained and discussed. While caveats of this model are well recognized, this pragmatic QRA could represent a useful tool for the French Food Safety Agency (AFSSA) to define recommendations in case of water resource contamination by C. parvum whose infectivity is comparable to the IOWA strain.     

Fractional Poisson—A Simple Dose‐Response Model for Human Norovirus

This study utilizes old and new Norovirus (NoV) human challenge data to model the dose‐response relationship for human NoV infection. The combined data set is used to update estimates from a previously published beta‐Poisson dose‐response model that includes parameters for virus aggregation and for a beta‐distribution that describes variable susceptibility among hosts. The quality of the beta‐Poisson model is examined and a simpler model is proposed. The new model (fractional Poisson) characterizes hosts as either perfectly susceptible or perfectly immune, requiring a single parameter (the fraction of perfectly susceptible hosts) in place of the two‐parameter beta‐distribution. A second parameter is included to account for virus aggregation in the same fashion as it is added to the beta‐Poisson model. Infection probability is simply the product of the probability of nonzero exposure (at least one virus or aggregate is ingested) and the fraction of susceptible hosts. The model is computationally simple and appears to be well suited to the data from the NoV human challenge studies. The model's deviance is similar to that of the beta‐Poisson, but with one parameter, rather than two. As a result, the Akaike information criterion favors the fractional Poisson over the beta‐Poisson model. At low, environmentally relevant exposure levels (<100), estimation error is small for the fractional Poisson model; however, caution is advised because no subjects were challenged at such a low dose. New low‐dose data would be of great value to further clarify the NoV dose‐response relationship and to support improved risk assessment for environmentally relevant exposures.     

First-Order Reliability Analysis of Public Health Risk Assessment

This paper demonstrates a new methodology for probabilistic public health risk assessment using the first-order reliability method. The method provides the probability that incremental lifetime cancer risk exceeds a threshold level, and the probabilistic sensitivity quantifying the relative impact of considering the uncertainty of each random variable on the exceedance probability. The approach is applied to a case study given by Thompson et al. ⁽¹⁾ on cancer risk caused by ingestion of benzene-contaminated soil, and the results are compared to that of the Monte Carlo method. Parametric sensitivity analyses are conducted to assess the sensitivity of the probabilistic event with respect to the distribution parameters of the basic random variables, such as the mean and standard deviation. The technique is a novel approach to probabilistic risk assessment, and can be used in situations when Monte Carlo analysis is computationally expensive, such as when the simulated risk is at the tail of the risk probability distribution.     

Dynamic Updating of Labour Force Estimates: JARES

Abstract. In this paper a new algorithm is proposed in order to produce an automatic dynamic compound estimator of the labour force based on an interactive scheme. The proposed algorithm, JARES, is based on the probability estimator of Jaynes based on the notion of maximum entropy of a given probability distribution with a constraint on the average of an external information. The iterative scheme is based on the solution of a set of linear equations which represent the algebraic relationships between the weights and the estimates.     

Use of Risk Assessment and Likelihood Estimation to Analyze Spatial Distribution Pattern of Respiratory Infection Cases

Obvious spatial infection patterns are often observed in cases associated with airborne transmissible diseases. Existing quantitative infection risk assessment models analyze the observed cases by assuming a homogeneous infectious particle concentration and ignore the spatial infection pattern, which may cause errors. This study aims at developing an approach to analyze spatial infection patterns associated with infectious respiratory diseases or other airborne transmissible diseases using infection risk assessment and likelihood estimation. Mathematical likelihood, based on binomial probability, was used to formulate the retrospective component with some additional mathematical treatments. Together with an infection risk assessment model that can address spatial heterogeneity, the method can be used to analyze the spatial infection pattern and retrospectively estimate the influencing parameters causing the cases, such as the infectious source strength of the pathogen. A Varicella outbreak was selected to demonstrate the use of the new approach. The infectious source strength estimated by the Wells‐Riley concept using the likelihood estimation was compared with the estimation using the existing method. It was found that the maximum likelihood estimation matches the epidemiological observation of the outbreak case much better than the estimation under the assumption of homogeneous infectious particle concentration. Influencing parameters retrospectively estimated using the new approach can be used as input parameters in quantitative infection risk assessment of the disease under other scenarios. The approach developed in this study can also serve as an epidemiological tool in outbreak investigation. Limitations and further developments are also discussed.     

Comparative assessment of analytical approaches to quantify the risk for introduction of rare animal diseases: the example of avian influenza in Spain

Trade of animals and animal products imposes an uncertain and variable risk for exotic animal diseases introduction into importing countries. Risk analysis provides importing countries with an objective, transparent, and internationally accepted method for assessing that risk. Over the last decades, European Union countries have conducted probabilistic risk assessments quite frequently to quantify the risk for rare animal diseases introduction into their territories. Most probabilistic animal health risk assessments have been typically classified into one-level and multilevel binomial models. One-level models are more simple than multilevel models because they assume that animals or products originate from one single population. However, it is unknown whether such simplification may result in substantially different results compared to those obtained through the use of multilevel models. Here, data used on a probabilistic multilevel binomial model formulated to assess the risk for highly pathogenic avian influenza introduction into Spain were reanalyzed using a one-level binomial model and their outcomes were compared. An alternative ordinal model is also proposed here, which makes use of simpler assumptions and less information compared to those required by traditional one-level and multilevel approaches. Results suggest that, at least under certain circumstances, results of the one-level and ordinal approaches are similar to those obtained using multilevel models. Consequently, we argue that, when data are insufficient to run traditional probabilistic models, the ordinal approach presented here may be a suitable alternative to rank exporting countries in terms of the risk that they impose for the spread of rare animal diseases into disease-free countries.     

MULTIPERIOD SEARCH MODELS FOR AN UNKNOWN NUMBER OF VALUABLE OBJECTS

In this paper we examine multiperiod search models for cases in which the number of valuable objects is unknown. The objective is to maximize the expected total returns during the planning horizon, subject to an effort constraint. Using a Bayesian approach, we examine the model for three different priors for the number of valuable objects, and we show that the different priors (binomial, Poisson and negative binomial) lead to such conceptually different results as adaptive and nonadaptive optimal policies. The models can be applied to many areas including mineral explorations, marketing promotion activities and intelligence information.     

C2C环境中顾客重复购买行为的实证与建模

通过分析C2C商家的交易记录,发现单个商家的顾客重复购买次数呈幂律分布,这与重复购买理论以往得到的购买次数为负二项分布的结论不同.基于C2C交易的实际情况,建立了具有购买强化效应的购买概率模型,模型很好的解释了顾客重复购买率呈幂律分布的现象.实证和模型表明,C2C环境中,顾客购买次数的分布具有很长的尾部,大量顾客有低的购买次数,而少数顾客有很高的重复购买次数;模型还揭示了巨大的潜在顾客数量和顾客多次购买的强化效应是造成重复购买分布呈幂律形式的重要原因.     

多代新技术的最优投资策略和扩散研究——一种实物期权方法

本文通过将新技术的出现描述为泊松过程,在未来多代新技术和投资成本随新技术出现不断下降的情形下,通过新技术采纳的累积概率分布函数,研究企业最优的技术投资策略以及新技术的扩散过程。在分析未来两代新技术的情形时,对比净现值(NPV)法则下得到的企业最优投资策略,由于NPV法忽视了企业推迟投资的期权价值,企业在NPV方法下只能得到次优的决策。数字释例显示出企业的技术采纳行为如何受到创新速度、折现率、投资成本及其下降幅度的影响。进一步在无穷代新技术的情形下,得到了企业最迟投资时间的计算方法。本文模型可以用来预测现实中企业的投资策略,并为实证分析新技术的采纳和扩散过程提供了理论支持。     

Exploring the Potential for Multivariate Fragility Representations to Alter Flood Risk Estimates

In flood risk analysis, limitations in the multivariate statistical models adopted to model the hydraulic load have restricted the probability of a defense suffering structural failure to be expressed conditionally on a single hydraulic loading variable. This is an issue at the coastal level where multiple loadings act on defenses with the exact combination of loadings dictating their failure probabilities. Recently, a methodology containing a multivariate statistical model with the flexibility to robustly capture the dependence structure between the individual loadings was used to derive extreme nearshore loading conditions. Its adoption will permit the incorporation of more precise representations of a structure's vulnerability in future analyses. In this article, a fragility representation of a shingle beach, where the failure probability is expressed over a three‐dimensional loading parameter space—water level, wave height, and period—is derived at two localities. Within the approach, a Gaussian copula is used to capture any dependencies between the simplified geometric parameters of a beach's shape. Beach profiles are simulated from the copula and the failure probability, given the hydraulic load, determined by the reformulated Bradbury barrier inertia parameter model. At one site, substantial differences in the annual failure probability distribution are observed between the new and existing approaches. At the other, the beach only becomes vulnerable after a significant reduction of the crest height with its mean annual failure probability close to that presently predicted. It is concluded that further application of multivariate approaches is likely to yield more effective flood risk management.