Moment Independent Importance Measures: New Results and Analytical Test Cases

Moment independent methods for the sensitivity analysis of model output are attracting growing attention among both academics and practitioners. However, the lack of benchmarks against which to compare numerical strategies forces one to rely on ad hoc experiments in estimating the sensitivity measures. This article introduces a methodology that allows one to obtain moment independent sensitivity measures analytically. We illustrate the procedure by implementing four test cases with different model structures and model input distributions. Numerical experiments are performed at increasing sample size to check convergence of the sensitivity estimates to the analytical values.     

Health‐Economics Analyses Applied to ELF Electric and Magnetic Fields

Extremely low frequency electric and magnetic fields (ELF EMFs) are a common exposure for modern populations. The prevailing public‐health protection paradigm is that quantitative exposure limits are based on the established acute effects, whereas the possible chronic effects are considered too uncertain for quantitative limits, but might justify precautionary measures. The choice of precautionary measures can be informed by a health‐economics analysis (HEA). We consider four such analyses of precautionary measures that have been conducted at a national or state level in California, the Netherlands, the United Kingdom, and Israel. We describe the context of each analysis, examine how they deal with some of the more significant issues that arise, and present a comparison of the input parameters and assumptions used. The four HEAs are methodologically similar. The most significant qualitative choices that have to be made are what dose‐response relationship to assume, what allowance if any to make for uncertainty, and, for a CBA only, what diseases to consider, and all four analyses made similar choices. These analyses suggest that, on the assumptions made, there are some low‐cost measures, such as rephasing, that can be applied to transmission in some circumstances and that can be justifiable in cost‐benefit terms, but that higher cost measures, such as undergrounding, become unjustifiable. Of the four HEAs, those in the United Kingdom and Israel were influential in determining the country's EMF policy. In California and Netherlands, the HEA may well have informed the debate, but the policy chosen did not stem directly from the HEA.     

Sensitivity Analysis of Model Output with Input Constraints: A Generalized Rationale for Local Methods

In this work, we introduce a generalized rationale for local sensitivity analysis (SA) methods that allows to solve the problems connected with input constraints. Several models in use in the risk analysis field are characterized by the presence of deterministic relationships among the input parameters. However, SA issues related to the presence of constraints have been mainly dealt with in a heuristic fashion. We start with a systematic analysis of the effects of constraints. The findings can be summarized in the following three effects. (i) Constraints make it impossible to vary one parameter while keeping all others fixed. (ii) The model output becomes insensitive to a parameter if a constraint is solved for that parameter. (iii) Sensitivity analysis results depend on which parameter is selected as dependent. The explanation of these effects is found by proposing a result that leads to a natural extension of the local SA rationale introduced in Helton (1993) . We then extend the definitions of the Birnbaum, criticality, and the differential importance measures to the constrained case. In addition, a procedure is introduced that allows to obtain constrained sensitivity results at the same cost as in the absence of constraints. The application to a nonbinary event tree concludes the article, providing a numerical illustration of the above findings.     

Sensitivity Analysis of a Two‐Dimensional Quantitative Microbiological Risk Assessment: Keeping Variability and Uncertainty Separated

The aim of quantitative microbiological risk assessment is to estimate the risk of illness caused by the presence of a pathogen in a food type, and to study the impact of interventions. Because of inherent variability and uncertainty, risk assessments are generally conducted stochastically, and if possible it is advised to characterize variability separately from uncertainty. Sensitivity analysis allows to indicate to which of the input variables the outcome of a quantitative microbiological risk assessment is most sensitive. Although a number of methods exist to apply sensitivity analysis to a risk assessment with probabilistic input variables (such as contamination, storage temperature, storage duration, etc.), it is challenging to perform sensitivity analysis in the case where a risk assessment includes a separate characterization of variability and uncertainty of input variables. A procedure is proposed that focuses on the relation between risk estimates obtained by Monte Carlo simulation and the location of pseudo‐randomly sampled input variables within the uncertainty and variability distributions. Within this procedure, two methods are used—that is, an ANOVA‐like model and Sobol sensitivity indices—to obtain and compare the impact of variability and of uncertainty of all input variables, and of model uncertainty and scenario uncertainty. As a case study, this methodology is applied to a risk assessment to estimate the risk of contracting listeriosis due to consumption of deli meats.     

Resilience Analysis of Countries under Disasters Based on Multisource Data

Disasters occur almost daily in the world. Because emergencies frequently have no precedent, are highly uncertain, and can be very destructive, improving a country's resilience is an efficient way to reduce risk. In this article, we collected more than 20,000 historical data points from disasters from 207 countries to enable us to calculate the severity of disasters and the danger they pose to countries. In addition, 6 primary indices (disaster, personal attribute, infrastructure, economics, education, and occupation) including 38 secondary influencing factors are considered in analyzing the resilience of countries. Using these data, we obtained the danger, expected number of deaths, and resilience of all 207 countries. We found that a country covering a large area is more likely to have a low resilience score. Through sensitivity analysis of all secondary indices, we found that population density, frequency of disasters, and GDP are the three most critical factors affecting resilience. Based on broad‐spectrum resilience analysis of the different continents, Oceania and South America have the highest resilience, while Asia has the lowest. Over the past 50 years, the resilience of many countries has been improved sharply, especially in developing countries. Based on our results, we analyze the comprehensive resilience and provide some optimal suggestions to efficiently improve resilience.     

A Protocol for the Global Sensitivity Analysis of Impact Assessment Models in Life Cycle Assessment

The life cycle assessment (LCA) framework has established itself as the leading tool for the assessment of the environmental impact of products. Several works have established the need of integrating the LCA and risk analysis methodologies, due to the several common aspects. One of the ways to reach such integration is through guaranteeing that uncertainties in LCA modeling are carefully treated. It has been claimed that more attention should be paid to quantifying the uncertainties present in the various phases of LCA. Though the topic has been attracting increasing attention of practitioners and experts in LCA, there is still a lack of understanding and a limited use of the available statistical tools. In this work, we introduce a protocol to conduct global sensitivity analysis in LCA. The article focuses on the life cycle impact assessment (LCIA), and particularly on the relevance of global techniques for the development of trustable impact assessment models. We use a novel characterization model developed for the quantification of the impacts of noise on humans as a test case. We show that global SA is fundamental to guarantee that the modeler has a complete understanding of: (i) the structure of the model and (ii) the importance of uncertain model inputs and the interaction among them.     

Adoption of Individual Flood Damage Mitigation Measures in New York City: An Extension of Protection Motivation Theory

This study offers insights into factors of influence on the implementation of flood damage mitigation measures by more than 1,000 homeowners who live in flood‐prone areas in New York City. Our theoretical basis for explaining flood preparedness decisions is protection motivation theory, which we extend using a variety of other variables that can have an important influence on individual decision making under risk, such as risk attitudes, time preferences, social norms, trust, and local flood risk management policies. Our results in relation to our main hypothesis are as follows. Individuals who live in high flood risk zones take more flood‐proofing measures in their home than individuals in low‐risk zones, which suggests the former group has a high threat appraisal. With regard to coping appraisal variables, we find that a high response efficacy and a high self‐efficacy play an important role in taking flood damage mitigation measures, while perceived response cost does not. In addition, a variety of behavioral characteristics influence individual decisions to flood‐proof homes, such as risk attitudes, time preferences, and private values of being well prepared for flooding. Investments in elevating one's home are mainly influenced by building code regulations and are negatively related with expectations of receiving federal disaster relief. We discuss a variety of policy recommendations to improve individual flood preparedness decisions, including incentives for risk reduction through flood insurance, and communication campaigns focused on coping appraisals and informing people about flood risk they face over long time horizons.     

Risk Management of Domino Effects Considering Dynamic Consequence Analysis

Domino effects are low‐probability high‐consequence accidents causing severe damage to humans, process plants, and the environment. Because domino effects affect large areas and are difficult to control, preventive safety measures have been given priority over mitigative measures. As a result, safety distances and safety inventories have been used as preventive safety measures to reduce the escalation probability of domino effects. However, these safety measures are usually designed considering static accident scenarios. In this study, we show that compared to a static worst‐case accident analysis, a dynamic consequence analysis provides a more rational approach for risk assessment and management of domino effects. This study also presents the application of Bayesian networks and conflict analysis to risk‐based allocation of chemical inventories to minimize the consequences and thus to reduce the escalation probability. It emphasizes the risk management of chemical inventories as an inherent safety measure, particularly in existing process plants where the applicability of other safety measures such as safety distances is limited.     

Modeling Benzene Pharmacokinetics Across Three Sets of Animal Data: Parametric Sensitivity and Risk Implications

Typically, the uncertainty affecting the parameters of physiologically based pharmacokinetic (PBPK) models is ignored because it is not currently practical to adjust their values using classical parameter estimation techniques. This issue of parametric variability in a physiological model of benzene pharmacokinetics is addressed in this paper. Monte Carlo simulations were used to study the effects on the model output arising from variability in its parameters. The output was classified into two categories, depending on whether the output of the model on a particular run was judged to be generally consistent with published experimental data. Statistical techniques were used to examine sensitivity and interaction in the parameter space. The model was evaluated against the data from three different experiments in order to test for the structural adequacy of the model and the consistency of the experimental results. The regions of the parameter space associated with various inhalation and gavage experiments are distinct, and the model as presently structured cannot adequately represent the outcomes of all experiments. Our results suggest that further effort is required to discern between the structural adequacy of the model and the consistency of the experimental results. The impact of our results on the risk assessment process for benzene is also examined.     

Sensitivity Analysis for Importance Assessment

We review briefly some examples that would support an extended role for quantitative sensitivity analysis in the context of model-based analysis (Section 1). We then review what features a quantitative sensitivity analysis needs to have to play such a role (Section 2). The methods that meet these requirements are described in Section 3; an example is provided in Section 4. Some pointers to further research are set out in Section 5.     

Rural Nevada and Climate Change: Vulnerability,Beliefs, and Risk Perception

In this article, we present the results of a study investigating the influence of vulnerability to climate change as a function of physical vulnerability, sensitivity, and adaptive capacity on climate change risk perception. In 2008/2009, we surveyed Nevada ranchers and farmers to assess their climate change‐related beliefs, and risk perceptions, political orientations, and socioeconomic characteristics. Ranchers’ and farmers’ sensitivity to climate change was measured through estimating the proportion of their household income originating from highly scarce water‐dependent agriculture to the total income. Adaptive capacity was measured as a combination of the Social Status Index and the Poverty Index. Utilizing water availability and use, and population distribution GIS databases; we assessed water resource vulnerability in Nevada by zip code as an indicator of physical vulnerability to climate change. We performed correlation tests and multiple regression analyses to examine the impact of vulnerability and its three distinct components on risk perception. We find that vulnerability is not a significant determinant of risk perception. Physical vulnerability alone also does not impact risk perception. Both sensitivity and adaptive capacity increase risk perception. While age is not a significant determinant of it, gender plays an important role in shaping risk perception. Yet, general beliefs such as political orientations and climate change‐specific beliefs such as believing in the anthropogenic causes of climate change and connecting the locally observed impacts (in this case drought) to climate change are the most prominent determinants of risk perception.     

Measuring Uncertainty Importance: Investigation and Comparison of Alternative Approaches

Uncertainty importance measures are quantitative tools aiming at identifying the contribution of uncertain inputs to output uncertainty. Their application ranges from food safety (Frey & Patil (2002)) to hurricane losses (Iman et al. (2005a, 2005b)). Results and indications an analyst derives depend on the method selected for the study. In this work, we investigate the assumptions at the basis of various indicator families to discuss the information they convey to the analyst/decisionmaker. We start with nonparametric techniques, and then present variance-based methods. By means of an example we show that output variance does not always reflect a decisionmaker state of knowledge of the inputs. We then examine the use of moment-independent approaches to global sensitivity analysis, i.e., techniques that look at the entire output distribution without a specific reference to its moments. Numerical results demonstrate that both moment-independent and variance-based indicators agree in identifying noninfluential parameters. However, differences in the ranking of the most relevant factors show that inputs that influence variance the most are not necessarily the ones that influence the output uncertainty distribution the most.     

On the Local Sensitivity Analysis of the Inoperability Input‐Output Model

Natural and man‐made disasters are currently a source of major concern for contemporary societies. In order to understand their economic impacts, the inoperability input‐output model has recently gained recognition among scholars. In a recent paper, Percoco (2006) has proposed an extension of the model to map the technologically most important sectors through so‐called fields of influence. In the present note we aim to show that this importance measure also has a clear connection with local sensitivity analysis theory.     

Asteroid Risk Assessment: A Probabilistic Approach

Following the 2013 Chelyabinsk event, the risks posed by asteroids attracted renewed interest, from both the scientific and policy‐making communities. It reminded the world that impacts from near‐Earth objects (NEOs), while rare, have the potential to cause great damage to cities and populations. Point estimates of the risk (such as mean numbers of casualties) have been proposed, but because of the low‐probability, high‐consequence nature of asteroid impacts, these averages provide limited actionable information. While more work is needed to further refine its input distributions (e.g., NEO diameters), the probabilistic model presented in this article allows a more complete evaluation of the risk of NEO impacts because the results are distributions that cover the range of potential casualties. This model is based on a modularized simulation that uses probabilistic inputs to estimate probabilistic risk metrics, including those of rare asteroid impacts. Illustrative results of this analysis are presented for a period of 100 years. As part of this demonstration, we assess the effectiveness of civil defense measures in mitigating the risk of human casualties. We find that they are likely to be beneficial but not a panacea. We also compute the probability—but not the consequences—of an impact with global effects (“cataclysm”). We conclude that there is a continued need for NEO observation, and for analyses of the feasibility and risk‐reduction effectiveness of space missions designed to deflect or destroy asteroids that threaten the Earth.     

Should Cities Invest in Sheltering‐in‐Place Measures Against Chlorine Truck Attacks by Terrorists?

After an intentional release of chlorine in an office district, public responses such as sheltering‐in‐place could save many lives if rapid enough. However, previous work does not estimate how fast and effective such responses would be for several possible investments in attack detection, public alert, and building ventilation, nor whether such measures would be cost effective. We estimate public response times with investment options in place, and resulting changes in fatalities as well as system costs, including false alarm costs, and cost effectiveness in terms of cost per net death avoided. The measures do have life‐saving potential, especially if all response times are at or near the lower limits of the ranges assumed in this article. However, due to uncertainties, it is not clear that responses would be rapid enough to save many people. In some cases total fatalities would increase, since sheltering after chlorine vapor has already entered buildings can increase occupants’ chlorine exposure. None of the options considered have median cost per statistical life saved meeting a cost‐effectiveness threshold of $6.5 million across all of the chlorine exposure dose‐response and ingress‐delay models considered here, even if there were one attack per year in the area covered by the system. Given these and other issues discussed in this article, at this point investments to improve sheltering‐in‐place capability appear not to be robust strategies for reducing fatalities from chlorine attack in an office district.     

Unsold Versus Unbought Commitment: Minimum Total Commitment Contracts with Nonzero Setup Costs

We study a minimum total commitment (MTC) contract embedded in a finite‐horizon periodic‐review inventory system. Under this contract, the buyer commits to purchase a minimum quantity of a single product from the supplier over the entire planning horizon. We consider nonstationary demand and per‐unit cost, discount factor, and nonzero setup cost. Because the formulations used in existing literature are unable to handle our setting, we develop a new formulation based on a state transformation technique using unsold commitment instead of unbought commitment as state variable. We first revisit the zero setup cost case and show that the optimal ordering policy is an unsold‐commitment‐dependent base‐stock policy. We also provide a simpler proof of the optimality of the dual base‐stock policy. We then study the nonzero setup cost case and prove a new result, that the optimal solution is an unsold‐commitment‐dependent (s, S) policy. We further propose two heuristic policies, which numerical tests show to perform very well. We also discuss two extensions to show the generality of our method's effectiveness. Finally, we use our results to examine the effect of different contract terms such as duration, lead time, and commitment on buyer's cost. We also compare total supply chain profits under periodic commitment, MTC, and no commitment.     

Using Real‐Time Decision Tools to Improve Distributed Decision‐Making Capabilities in High‐Magnitude Crisis Situations*

Multi‐organizational collaborative decision making in high‐magnitude crisis situations requires real‐time information sharing and dynamic modeling for effective response. Information technology (IT) based decision support tools can play a key role in facilitating such effective response. We explore one promising class of decision support tools based on machine learning, known as support vector machines (SVM), which have the capability to dynamically model and analyze decision processes. To examine this capability, we use a case study with a design science approach to evaluate improved decision‐making effectiveness of an SVM algorithm in an agent‐based simulation experimental environment. Testing and evaluation of real‐time decision support tools in simulated environments provides an opportunity to assess their value under various dynamic conditions. Decision making in high‐magnitude crisis situations involves multiple different patterns of behavior, requiring the development, application, and evaluation of different models. Therefore, we employ a multistage linear support vector machine (MLSVM) algorithm that permits partitioning decision maker response into behavioral subsets, which can then individually model and examine their diverse patterns of response behavior. The results of our case study indicate that our MLSVM is clearly superior to both single stage SVMs and traditional approaches such as linear and quadratic discriminant analysis for understanding and predicting behavior. We conclude that machine learning algorithms show promise for quickly assessing response strategy behavior and for providing the capability to share information with decision makers in multi‐organizational collaborative environments, thus supporting more effective decision making in such contexts.     

Use of Fuzzy Evidential Reasoning in Maritime Security Assessment

Over the last few years, there has been a growing international recognition that the security performance of the maritime industry needs to be reviewed on an urgent basis. A large number of optional maritime security control measures have been proposed through various regulations and publications in the post-9/11 era. There is a strong need for a sound and generic methodology, which is capable of taking into account multiple selection criteria such as the cost effectiveness of the measures based on reasonable security assessment. The use of traditional risk assessment and decision-making approaches to deal with potential terrorism threats in a maritime security area reveals two major challenges. They are lack of capability of analyzing security in situations of high-level uncertainty and lack of capability of processing diverse data in a utility form suitable as input to a risk inference mechanism. To deal with such difficulties, this article proposes a subjective security-based assessment and management framework using fuzzy evidential reasoning (ER) approaches. Consequently, the framework can be used to assemble and process subjective risk assessment information on different aspects of a maritime transport system from multiple experts in a systematic way. Outputs of this model can also provide decisionmakers with a transparent tool to evaluate maritime security policy options for a specific scenario in a cost-effective manner.     

Sensitivity and Uncertainty Studies of the CRAC2 Computer Code

We have studied the sensitivity of health impacts from nuclear reactor accidents, as predicted by the CRAC2 computer code, to the following sources of uncertainty: (1) the model for plume rise, (2) the model for wet deposition, (3) the meteorological bin-sampling procedure for selecting weather sequences with rain, (4) the dose conversion factors for inhalation as affected by uncertainties in the particle size of the carrier aerosol and the clearance rates of radionuclides from the respiratory tract, (5) the weathering half-time for external ground-surface exposure, and (6) the transfer coefficients for terrestrial foodchain pathways. Predicted health impacts usually showed little sensitivity to use of an alternative plume-rise model or a modified rain-bin structure in bin-sampling. Health impacts often were quite sensitive to use of an alternative wet-deposition model in single-trial runs with rain during plume passage, but were less sensitive to the model in bin-sampling runs. Uncertainties in the inhalation dose conversion factors had important effects on early injuries in single-trial runs. Latent cancer fatalities were moderately sensitive to uncertainties in the weathering half-time for ground-surface exposure, but showed little sensitivity to the transfer coefficients for terrestrial foodchain pathways. Sensitivities of CRAC2 predictions to uncertainties in the models and parameters also depended on the magnitude of the source term, and some of the effects on early health effects were comparable to those that were due only to selection of different sets of weather sequences in bin-sampling.     

On the Sensitivity Analysis of the IIM: A Rejoinder

In this note I reply to the comments by Haimes et al. on my paper on the sensitivity analysis of the inoperability input‐output model. I make the case for a moment‐independent sensitivity analysis.