Probability Elicitation Under Severe Time Pressure: A Rank‐Based Method

Probability elicitation protocols are used to assess and incorporate subjective probabilities in risk and decision analysis. While most of these protocols use methods that have focused on the precision of the elicited probabilities, the speed of the elicitation process has often been neglected. However, speed is also important, particularly when experts need to examine a large number of events on a recurrent basis. Furthermore, most existing elicitation methods are numerical in nature, but there are various reasons why an expert would refuse to give such precise ratio‐scale estimates, even if highly numerate. This may occur, for instance, when there is lack of sufficient hard evidence, when assessing very uncertain events (such as emergent threats), or when dealing with politicized topics (such as terrorism or disease outbreaks). In this article, we adopt an ordinal ranking approach from multicriteria decision analysis to provide a fast and nonnumerical probability elicitation process. Probabilities are subsequently approximated from the ranking by an algorithm based on the principle of maximum entropy, a rule compatible with the ordinal information provided by the expert. The method can elicit probabilities for a wide range of different event types, including new ways of eliciting probabilities for stochastically independent events and low‐probability events. We use a Monte Carlo simulation to test the accuracy of the approximated probabilities and try the method in practice, applying it to a real‐world risk analysis recently conducted for DEFRA (the U.K. Department for the Environment, Farming and Rural Affairs): the prioritization of animal health threats.     

Correlations Between Parameters in Risk Models: Estimation and Propagation of Uncertainty by Markov Chain Monte Carlo

Monte Carlo simulation has become the accepted method for propagating parameter uncertainty through risk models. It is widely appreciated, however, that correlations between input variables must be taken into account if models are to deliver correct assessments of uncertainty in risk. Various two-stage methods have been proposed that first estimate a correlation structure and then generate Monte Carlo simulations, which incorporate this structure while leaving marginal distributions of parameters unchanged. Here we propose a one-stage alternative, in which the correlation structure is estimated from the data directly by Bayesian Markov Chain Monte Carlo methods. Samples from the posterior distribution of the outputs then correctly reflect the correlation between parameters, given the data and the model. Besides its computational simplicity, this approach utilizes the available evidence from a wide variety of structures, including incomplete data and correlated and uncorrelated repeat observations. The major advantage of a Bayesian approach is that, rather than assuming the correlation structure is fixed and known, it captures the joint uncertainty induced by the data in all parameters, including variances and covariances, and correctly propagates this through the decision or risk model. These features are illustrated with examples on emissions of dioxin congeners from solid waste incinerators.     

On the Rank-Based Selection Strategy for the Group Interview Problem*

For the so-called group interview problem in which several groups of choice alternatives are presented sequentially to the decision maker, the optimal selection strategy is derived that minimizes the expected rank of the selected choice or purchased product. For the case in which the sequence of groups can be rearranged by the decision maker, a simple heuristic procedure is proposed for obtaining a near-optimal sequence of groups, and the performance of the heuristic procedure in a Monte Carlo simulation is accessed. According to the heuristic procedure, the consumer is advised to visit smaller stores first and then move to larger stores later to increase the likelihood of finding a better product. Finally, the optimal selection strategy and the heuristic procedure are compared with those proposed by Chun, Moskowitz, and Plante (1993) and the problem of locating a new store in an area where there are several competing stores is discussed. The optimal selection strategy and the heuristic procedure can be applied to many sequential decision problems such as the consumer search and purchase process.     

Monte Carlo Sampling for Generalized Knowledge Dependence with Application to Human Reliability

A general discussion of knowledge dependence in risk calculations shows that the assumption of independence underlying standard Monte Carlo simulation in uncertainty analysis is frequently violated. A model is presented for performing Monte Carlo simulation when the variabilities of the component failure probabilities are either negatively or positively coupled. The model is applied to examples in human reliability analysis and the results are compared to the results of Sandia Laboratories as published in the Peer Review Study and to recalculations using more recent methods of uncertainty analysis.     

Extreme Risk Analysis of Interdependent Economic and Infrastructure Sectors

Willful attacks or natural disasters pose extreme risks to sectors of the economy. An extreme-event analysis extension is proposed for the Inoperability Input-Output Model (IIM) and the Dynamic IIM (DIIM), which are analytical methodologies for assessing the propagated consequences of initial disruptions to a set of sectors. The article discusses two major risk categories that the economy typically experiences following extreme events: (i) significant changes in consumption patterns due to lingering public fear and (ii) adjustments to the production outputs of the interdependent economic sectors that are necessary to match prevailing consumption levels during the recovery period. Probability distributions associated with changes in the consumption of directly affected sectors are generated based on trends, forecasts, and expert evidence to assess the expected losses of the economy. Analytical formulations are derived to quantify the extreme risks associated with a set of initially affected sectors. In addition, Monte Carlo simulation is used to handle the more complex calculations required for a larger set of sectors and general types of probability distributions. A two-sector example is provided at the end of the article to illustrate the proposed extreme risk model formulations.     

Accounting for Both Random Errors and Systematic Errors in Uncertainty Propagation Analysis of Computer Models Involving Experimental Measurements with Monte Carlo Methods

A Monte Carlo method is presented to study the effect of systematic and random errors on computer models mainly dealing with experimental data. It is a common assumption in this type of models (linear and nonlinear regression, and nonregression computer models) involving experimental measurements that the error sources are mainly random and independent with no constant background errors (systematic errors). However, from comparisons of different experimental data sources evidence is often found of significant bias or calibration errors. The uncertainty analysis approach presented in this work is based on the analysis of cumulative probability distributions for output variables of the models involved taking into account the effect of both types of errors. The probability distributions are obtained by performing Monte Carlo simulation coupled with appropriate definitions for the random and systematic errors. The main objectives are to detect the error source with stochastic dominance on the uncertainty propagation and the combined effect on output variables of the models. The results from the case studies analyzed show that the approach is able to distinguish which error type has a more significant effect on the performance of the model. Also, it was found that systematic or calibration errors, if present, cannot be neglected in uncertainty analysis of models dependent on experimental measurements such as chemical and physical properties. The approach can be used to facilitate decision making in fields related to safety factors selection, modeling, experimental data measurement, and experimental design.     

A decision support methodology for strategic planning in maritime transportation

This paper presents a decision support methodology for strategic planning in tramp and industrial shipping. The proposed methodology combines simulation and optimization, where a Monte Carlo simulation framework is built around an optimization-based decision support system for short-term routing and scheduling. The simulation proceeds by considering a series of short-term routing and scheduling problems using a rolling horizon principle where information is revealed as time goes by. The approach is flexible in the sense that it can easily be configured to provide decision support for a wide range of strategic planning problems, such as fleet size and mix problems, analysis of long-term contracts and contract terms. The methodology is tested on a real case for a major Norwegian shipping company. The methodology provided valuable decision support on important strategic planning problems for the shipping company.     

Estimation of Error and Bias in Bayesian Monte Carlo Decision Analysis Using the Bootstrap

Bayesian Monte Carlo (BMC) decision analysis adopts a sampling procedure to estimate likelihoods and distributions of outcomes, and then uses that information to calculate the expected performance of alternative strategies, the value of information, and the value of including uncertainty. These decision analysis outputs are therefore subject to sample error. The standard error of each estimate and its bias, if any, can be estimated by the bootstrap procedure. The bootstrap operates by resampling (with replacement) from the original BMC sample, and redoing the decision analysis. Repeating this procedure yields a distribution of decision analysis outputs. The bootstrap approach to estimating the effect of sample error upon BMC analysis is illustrated with a simple value-of-information calculation along with an analysis of a proposed control structure for Lake Erie. The examples show that the outputs of BMC decision analysis can have high levels of sample error and bias.     

Influence of Safety Measures on the Risks of Transporting Dangerous Goods Through Road Tunnels

Quantitative risk assessment (QRA) models are used to estimate the risks of transporting dangerous goods and to assess the merits of introducing alternative risk reduction measures for different transportation scenarios and assumptions. A comprehensive QRA model recently was developed in Europe for application to road tunnels. This model can assess the merits of a limited number of "native safety measures." In this article, we introduce a procedure for extending its scope to include the treatment of a number of important "nonnative safety measures" of interest to tunnel operators and decisionmakers. Nonnative safety measures were not included in the original model specification. The suggested procedure makes use of expert judgment and Monte Carlo simulation methods to model uncertainty in the revised risk estimates. The results of a case study application are presented that involve the risks of transporting a given volume of flammable liquid through a 10-km road tunnel.     

基于投影降维技术的期权组合非线性VaR模型

高维期权组合VaR值的计算时间和计算工作量随着市场风险因子维数的增加而迅速增加.为此,引入投影降维技术,用少数几个风险因子来解释高维期权组合总的风险,并结合快速卷积方法,建立了基于投影降维技术的市场风险因子呈厚尾分布情形下的期权组合非线性VaR模型,达到减少计算时间和计算工作量的目的,同时期权组合价值变化的信息又没有太大的损失.数值结果表明,投影降维技术能够达到与快速卷积方法、Monte-Carlo方法差不多的估算精度,而计算效率明显优于快速卷积方法、Monte-Carlo方法,计算时间和计算工作量明显减少.     

PROCEDURES TO INCREASE THE VALIDITY OF SUBJECTIVE PROBABILITY ESTIMATES

A decision making model is often very sensitive to the subjective probability estimates that are used. To reduce this sensitivity, it is necessary to utilize elicitation procedures that yield more valid estimates and increase the decision maker's confidence in the estimates. This paper discusses an experiment in which the subjects were asked to estimate the areas of various squares. Two procedures were evaluated. In one procedure, the subjects were told that estimates were distributed typically around the true value in accordance with the normal probability distribution. In the other, the subjects were asked to estimate the length as a component that could be used to calculate the area. The results indicate that the normal error model is a reasonable representation of the estimation procedure. Both procedures provided estimates with significant validity. There is also an indication that the procedures reduce bias and that both procedures result in more consistent estimates when the sizes of the squares are varied.     

Random Number Generation from Right-Skewed, Symmetric, and Left-Skewed Distributions

Monte Carlo simulations have become a mainstream technique for environmental and technical risk assessments. Because their results are dependent on the quality of the involved input distributions, it is important to identify distributions that are flexible enough to model all relevant data yet efficient enough to allow thousands of evaluations necessary in a typical simulation analysis. It has been shown in recent years that the S-distribution provides accurate representations for frequency data that are symmetric or skewed to either side. This flexibility makes the S-distribution an ideal candidate for Monte Carlo analyses. To use the distribution effectively, methods must be available for drawing S-distributed random numbers. Such a method is proposed here. It is shown that S-distributed random numbers can be efficiently generated from a simple algebraic formula whose coefficients are tabulated. The method is shown step by step and illustrated with a detailed example. (The tables are accessible in electronic form in the FTP parent directory at http:@www.musc.edu/voiteo/ftp/.)     

基于多因子LIBOR模型的CMS数字范围债券定价

论文在鞅论和测度变换的基础上,在多因子LIBOR市场模型的框架下,通过二阶变差的方法获得了CMS利率的近似分布,巧妙的解决了CMS利率在LIBOR市场模型下不满足对数正态分布的问题。在此基础上,利用CMS利率的近似概率分布,求解得出CMS范围数字债券的定价,避免了Monte Carlo大数据模拟的情况,在对浮动利率产品进行研究的过程中,论文使用了两种不同的方法进行比较,主要是引理法和Girsanov法,这为投资者的定价过程提供了选择,有利于投资者获得更好的投资回报。     

AbSRiM: An Agent‐Based Security Risk Management Approach for Airport Operations

Security risk management is essential for ensuring effective airport operations. This article introduces AbSRiM, a novel agent‐based modeling and simulation approach to perform security risk management for airport operations that uses formal sociotechnical models that include temporal and spatial aspects. The approach contains four main steps: scope selection, agent‐based model definition, risk assessment, and risk mitigation. The approach is based on traditional security risk management methodologies, but uses agent‐based modeling and Monte Carlo simulation at its core. Agent‐based modeling is used to model threat scenarios, and Monte Carlo simulations are then performed with this model to estimate security risks. The use of the AbSRiM approach is demonstrated with an illustrative case study. This case study includes a threat scenario in which an adversary attacks an airport terminal with an improvised explosive device. The approach provides a promising way to include important elements, such as human aspects and spatiotemporal aspects, in the assessment of risk. More research is still needed to better identify the strengths and weaknesses of the AbSRiM approach in different case studies, but results demonstrate the feasibility of the approach and its potential.     

我国上市银行信用溢价的实证研究

在改进KMV模型、采用信用溢价直观度量银行信用风险的基础上,通过MonteCarlo模拟法估计12家样本银行信用风险的VaR和CVaR值,并与历史模拟法的度量结果进行比较。研究结果表明,历史模拟法高估了银行所面临的信用风险;在样本银行中,中国银行最容易发生极端信用事件,工商银行则相反。     

Combining Experts: Decomposition and Aggregation Order

In this article we ask, if quantities in an elicitation have been decomposed, is it better to combine experts before or after recomposing the quantities? We find that combining experts earlier, before recomposition of the quantities, leads to smaller errors with less variance. A simulation shows that these differences may be quite small on average; while an application to actual data shows that the differences can be significant in individual decision problems.     

A SIMULATION OF THE EFFECTS OF ALTERNATIVE RULE SYSTEMS FOR JAI ALAI*

The inequities of the present system of rules in jai alai are documented on the basis of empirical information and theoretical results from a Monte Carlo simulation model. Some suggestions are made for changing the rules in order to make the game more equitable for both players and bettors. The simulation model is used to compare the effectiveness of the suggested rules with that of the present rules.     

Integrating performance and risk aspects of supply chain design processes

Abstract

Supply chain design is a complex and relatively poorly structured process, involving choosing many decisional parameters and it usually requires consideration of numerous sources of uncertainty. Many conventional processes of supply chain design involve taking a deterministic approach, using point estimates, on important measures of supply chain effectiveness such as cost, quality, delivery reliability and service levels. Supply chain disruptions are often separately considered as risks, both in the research literature and in practice, meaning that a purely traditional risk management and risk minimization approach is taken. We have developed and applied an approach that combines the intellect and experience of the supply chain designer with the power of evaluation provided by a Monte Carlo simulation model, which uses decision analysis techniques to explicitly incorporate the full spectrum of uncertain quantities across the set of alternative supply chain designs being considered. After defining and setting out the general decision variables and uncertainty factors for 16 distinct supply chain design decision categories, we then apply that approach to combine the decision-makers’ heuristics with the probabilistic modeling approach, iteratively, to achieve the best of both elements of such an approach. This novel approach to fully integrating performance and risk elements of supply chain designs is then illustrated with a case study. Finally, we call for further developmental research and field work to refine this approach.     

基于MCMC的金融市场风险VaR的估计

针对现有 Va R计算中主流方法的缺陷 ,创新性地提出了一种基于马尔科夫链蒙特卡洛(Markov Chain Monte Carlo,MCMC)模拟的 Va R计算方法 ,以克服传统 Monte Carlo模拟的高维、静态性缺陷 ,提高估算精度 .通过对美元国债的实证分析和计算 ,验证了 MCMC方法的优越性 .     

Analysis of antithetic sequences in flowshop scheduling to minimize makespan

The antithetic properties of flowshop sequences are investigated to improve the classical Monte Carlo method for solving the n -job, m -machine problem with minimization of makespan. The major issues considered are (1) establishing a negative correlation of the makespan values of forward and reverse sequences; (2) developing the Antithetical Monte Carlo (AMC) method, which can be used to quickly estimate the mean of the makespan distribution by exploiting the antithetic property of sequences; (3) using AMC to find low makespan values; (4) determining a threshold value of makespan beyond which it would be likely to find an optimal or near optimal makespan when reversing a sequence. Statistical tests indicate that the performance of AMC is superior to that of the classical Monte Carlo method. Possible applications of this concept are discussed including extensions to other mathematical problems with antithetic properties.