The Effects of Presenting Imprecise Probabilities in Intelligence Forecasts

How to assess and present analytic uncertainty to policymakers has emerged as an important topic in risk and policy analysis. Due to the complexity and deep uncertainty present in many forecasting domains, these reports are often fraught with analytic uncertainty. In three studies, we explore the effect of presenting probability assessments and analytic uncertainty through probability ranges. Participants were presented with mock intelligence forecasts that include narrative evidence as well as numerical probability assessments. Participants were sensitive to the ambiguity communicated through the confidence range. The narrative appeared to have a smaller effect on judgments when accompanied by a probability range as opposed to a point assessment. In one study, participants also thought that the probability range was more useful for decision making at a higher probability whereas the point estimate was more useful at a lower probability. When evaluating a forecast in hindsight, decisionmakers tended to report lower levels of blame and higher levels of source credibility for forecasts that reported ranges as compared to point assessments. These findings suggest that decisionmakers are not necessarily “ambiguity averse” in the forecasting context. Presenting ranges of probability may have distinct advantages as a way to communicate probability and analytic confidence to decisionmakers.     

Illustration of a Method to Incorporate Preference Uncertainty in Benefit–Cost Analysis

Benefit–cost analysis is widely used to evaluate alternative courses of action that are designed to achieve policy objectives. Although many analyses take uncertainty into account, they typically only consider uncertainty about cost estimates and physical states of the world, whereas uncertainty about individual preferences, thus the benefit of policy intervention, is ignored. Here, we propose a strategy to integrate individual uncertainty about preferences into benefit–cost analysis using societal preference intervals, which are ranges of values over which it is unclear whether society as a whole should accept or reject an option. To illustrate the method, we use preferences for implementing a smart grid technology to sustain critical electricity demand during a 24‐hour regional power blackout on a hot summer weekend. Preferences were elicited from a convenience sample of residents in Allegheny County, Pennsylvania. This illustrative example shows that uncertainty in individual preferences, when aggregated to form societal preference intervals, can substantially change society's decision. We conclude with a discussion of where preference uncertainty comes from, how it might be reduced, and why incorporating unresolved preference uncertainty into benefit–cost analyses can be important.     

基于证据推理的不确定多属性决策方法

针对基本属性权重的不确定性,以及基本属性与广义属性评价集的不一致性等问题,提出一种基于证据推理的不确定多属性决策方法,将证据推理算法推广到更一般的决策环境中.根据决策矩阵的信息熵客观地获得属性的权系数;而对于基本属性与广义属性评价集不一致的情况,则通过对基本属性分布评价的模糊化及模糊变换,合理地实现到广义分布评价的统一形式;最后应用证据推理算法得到整个方案集的排序.实例结果表明,该方法是可行的、有效的.     

Unquestioned Answers or Unanswered Questions: Beliefs About Science Guide Responses to Uncertainty in Climate Change Risk Communication

In two experimental studies we investigated the effect of beliefs about the nature and purpose of science (classical vs. Kuhnian models of science) on responses to uncertainty in scientific messages about climate change risk. The results revealed a significant interaction between both measured (Study 1) and manipulated (Study 2) beliefs about science and the level of communicated uncertainty on willingness to act in line with the message. Specifically, messages that communicated high uncertainty were more persuasive for participants who shared an understanding of science as debate than for those who believed that science is a search for absolute truth. In addition, participants who had a concept of science as debate were more motivated by higher (rather than lower) uncertainty in climate change messages. The results suggest that achieving alignment between the general public's beliefs about science and the style of the scientific messages is crucial for successful risk communication in science. Accordingly, rather than uncertainty always undermining the effectiveness of science communication, uncertainty can enhance message effects when it fits the audience's understanding of what science is.     

Facility Location: A Robust Optimization Approach

In this research, we apply robust optimization (RO) to the problem of locating facilities in a network facing uncertain demand over multiple periods. We consider a multi‐period fixed‐charge network location problem for which we find (1) the number of facilities, their location and capacities, (2) the production in each period, and (3) allocation of demand to facilities. Using the RO approach we formulate the problem to include alternate levels of uncertainty over the periods. We consider two models of demand uncertainty: demand within a bounded and symmetric multi‐dimensional box, and demand within a multi‐dimensional ellipsoid. We evaluate the potential benefits of applying the RO approach in our setting using an extensive numerical study. We show that the alternate models of uncertainty lead to very different solution network topologies, with the model with box uncertainty set opening fewer, larger facilities. Through sample path testing, we show that both the box and ellipsoidal uncertainty cases can provide small but significant improvements over the solution to the problem when demand is deterministic and set at its nominal value. For changes in several environmental parameters, we explore the effects on the solution performance.     

A Bayesian Semiparametric Model for Radiation Dose‐Response Estimation

In evaluating the risk of exposure to health hazards, characterizing the dose‐response relationship and estimating acceptable exposure levels are the primary goals. In analyses of health risks associated with exposure to ionizing radiation, while there is a clear agreement that moderate to high radiation doses cause harmful effects in humans, little has been known about the possible biological effects at low doses, for example, below 0.1 Gy, which is the dose range relevant to most radiation exposures of concern today. A conventional approach to radiation dose‐response estimation based on simple parametric forms, such as the linear nonthreshold model, can be misleading in evaluating the risk and, in particular, its uncertainty at low doses. As an alternative approach, we consider a Bayesian semiparametric model that has a connected piece‐wise‐linear dose‐response function with prior distributions having an autoregressive structure among the random slope coefficients defined over closely spaced dose categories. With a simulation study and application to analysis of cancer incidence data among Japanese atomic bomb survivors, we show that this approach can produce smooth and flexible dose‐response estimation while reasonably handling the risk uncertainty at low doses and elsewhere. With relatively few assumptions and modeling options to be made by the analyst, the method can be particularly useful in assessing risks associated with low‐dose radiation exposures.     

The Role of Task Uncertainty in IT Project Team Advice Networks

Advice seeking is often the most critical success factor in today's IT project teams. To understand how advice seekers are motivated, we integrate the antecedents of advice seeking—as defined by network theory (Granovetter, 1983)—into a cost/benefit model based on expectancy theory (Vroom, 1964). To contribute to the research on advice network formation, we integrate the role of task uncertainty—one of the defining characteristics of IT projects—into that research (Wallace & Keil, 2004). Based on a controlled quasi‐experiment, this study demonstrates that when task uncertainty is low, individuals with attractive personalities and similar demographics will be sought out for advice more frequently, regardless of their knowledge and resources (i.e., the benefits to the advice seekers). However, when task uncertainty is high, individuals with greater knowledge and access to resources are sought out more often in an advice network. These results provide clarity to prior research that has found mixed results concerning the effectiveness of the traditional antecedents to advice seeking (e.g., knowledge, power, and transactive memory) (e.g., Xu, Kim, & Kankanhalli, 2010a). In addition, project managers may choose to alter their team structure in order to optimize the advice network based on the anticipated level of IT project risk or task uncertainty.     

Impact of Demand Uncertainty on Stability of Supplier Alliances in Assembly Models

In their recent paper, Nagarajan and Sošić study an assembly supply chain in which n suppliers sell complementary components to a downstream assembler, who faces a price‐sensitive deterministic demand. Suppliers may form alliances, and each alliance then sells a kit of components to the assembler and determines the price for that kit. The assembler buys the components (kits) from the alliances and sets the selling price of the product. Nagarajan and Sošić consider three modes of competition—supplier Stackelberg, vertical Nash (VN), and assembler Stackelberg models—which correspond to different power structures in the market, and study stable supplier alliances when the assembler faces linear and isoelastic demand. In this paper, we study the impact that demand uncertainty has on stability results obtained in Nagarajan and Sošić. We first analyze models in which all decisions are made before the uncertainty is resolved, and show that the alliance of all suppliers remains stable when demand is isoelastic, or under Stackelberg models when demand is linear. However, demand uncertainty may change stability results when both parties make decisions simultaneously (VN model) and demand is linear. We then extend our results by considering scenarios in which some decisions may be postponed and made after the actual demand is known. When the ordering quantity can be determined after observing the true demand, we show that stable outcomes correspond to those obtained in the deterministic case and uncertainty has no impact on coalition stability; if only the assembler's pricing decision is postponed, we need additional conditions for stability results to carry over in the additive demand model.     

Epistemic Uncertainty in the Ranking and Categorization of Probabilistic Safety Assessment Model Elements: Issues and Findings

In this work, we study the effect of epistemic uncertainty in the ranking and categorization of elements of probabilistic safety assessment (PSA) models. We show that, while in a deterministic setting a PSA element belongs to a given category univocally, in the presence of epistemic uncertainty, a PSA element belongs to a given category only with a certain probability. We propose an approach to estimate these probabilities, showing that their knowledge allows to appreciate " the sensitivity of component categorizations to uncertainties in the parameter values " (U.S. NRC Regulatory Guide 1.174). We investigate the meaning and utilization of an assignment method based on the expected value of importance measures. We discuss the problem of evaluating changes in quality assurance, maintenance activities prioritization, etc. in the presence of epistemic uncertainty. We show that the inclusion of epistemic uncertainly in the evaluation makes it necessary to evaluate changes through their effect on PSA model parameters. We propose a categorization of parameters based on the Fussell-Vesely and differential importance (DIM) measures. In addition, issues in the calculation of the expected value of the joint importance measure are present when evaluating changes affecting groups of components. We illustrate that the problem can be solved using DIM. A numerical application to a case study concludes the work.     

Mitigating Supply Uncertainty: The Interplay Between Diversification and Pricing

We consider a firm's sourcing problem from one reliable supplier and one unreliable supplier in two price‐setting scenarios. In the committed pricing scenario, the firm makes the pricing decision before the supply uncertainty is resolved. In the responsive pricing scenario, the firm's pricing decision is made after the supply uncertainty is resolved. For the committed pricing scenario, we develop a condition on supply uncertainty that guarantees the unimodality of the firm's objective function. By comparing the firm's optimal diversification decisions in the two pricing scenarios, we examine the interplay of supply diversification strategy and responsive pricing strategy in mitigating supply uncertainty. While both strategies are effective in mitigating supply uncertainty, we show that they are not necessarily substitutes. The relationship between these two strategies depends on two adverse effects caused by supply uncertainty: the lost‐revenue effect and the lost‐goodwill effect. More specifically, when the lost‐revenue effect dominates the lost‐goodwill effect, these two strategies are complements; otherwise, they are substitutes. Furthermore, we examine the impact of market size, price sensitivity, supplier reliability, and failure rebate on the interplay between these two strategies, and discuss the implications of our results. Finally, we extend our analysis to the case of two unreliable suppliers and show that the insights regarding the interplay between diversification and pricing continue to hold.     

Deliberative Disjunction: Expert and Public Understanding of Outcome Uncertainty

Many environmental and risk management decisions are made jointly by technical experts and members of the public. Frequently, their task is to select from among management alternatives whose outcomes are subject to varying degrees of uncertainty. Although it is recognized that how this uncertainty is interpreted can significantly affect decision‐making processes and choices, little research has examined similarities and differences between expert and public understandings of uncertainty. We present results from a web‐based survey that directly compares expert and lay interpretations and understandings of different expressions of uncertainty in the context of evaluating the consequences of proposed environmental management actions. Participants responded to two hypothetical but realistic scenarios involving trade‐offs between environmental and other objectives and were asked a series of questions about their comprehension of the uncertainty information, their preferred choice among the alternatives, and the associated difficulty and amount of effort. Results demonstrate that experts and laypersons tend to use presentations of numerical ranges and evaluative labels differently; interestingly, the observed differences between the two groups were not explained by differences in numeracy or concerns for the predicted environmental losses. These findings question many of the usual presumptions about how uncertainty should be presented as part of deliberative risk‐ and environmental‐management processes.     

Advancing Theory in Entrepreneurship from the Lens of Operations Management

Early writings in economics describe the entrepreneur's role in terms of bearing the uncertainty inherent in new undertakings. Much of the research published in the pages of Production and Operations Management deals with management under uncertainty. The shared concerns over the impacts of multiple types of uncertainty suggest that research on Operations Management (OM) can play a role in the development of theory in entrepreneurship. We discuss aspects of such a role from two perspectives. First, we consider several topics in the OM literature that have clear applications or parallels in entrepreneurship. These topics include innovation, the management of technology, new product development, flexibility, and hedging strategies. Understanding these topical connections should aid in the development of tools and applications central to the practice of entrepreneurship. On another level, when we consider how the approaches to many of these topics in OM are grounded in theory adapted from Operations Research and Economics we argue that these same roots can be used as starting points for the development of theory in entrepreneurship. As examples, we will argue that the theoretical bases supporting robust optimization, stochastic dynamic programming, and even Total Quality Management can also serve as foundations of theories about the roles, practice, and behaviors of entrepreneurs.     

A Bayesian Method to Mine Spatial Data Sets to Evaluate the Vulnerability of Human Beings to Catastrophic Risk

Vulnerability of human beings exposed to a catastrophic disaster is affected by multiple factors that include hazard intensity, environment, and individual characteristics. The traditional approach to vulnerability assessment, based on the aggregate‐area method and unsupervised learning, cannot incorporate spatial information; thus, vulnerability can be only roughly assessed. In this article, we propose Bayesian network (BN) and spatial analysis techniques to mine spatial data sets to evaluate the vulnerability of human beings. In our approach, spatial analysis is leveraged to preprocess the data; for example, kernel density analysis (KDA) and accumulative road cost surface modeling (ARCSM) are employed to quantify the influence of geofeatures on vulnerability and relate such influence to spatial distance. The knowledge‐ and data‐based BN provides a consistent platform to integrate a variety of factors, including those extracted by KDA and ARCSM to model vulnerability uncertainty. We also consider the model's uncertainty and use the Bayesian model average and Occam's Window to average the multiple models obtained by our approach to robust prediction of the risk and vulnerability. We compare our approach with other probabilistic models in the case study of seismic risk and conclude that our approach is a good means to mining spatial data sets for evaluating vulnerability.     

Sourcing Decisions with Competitive Suppliers and Imperfect Information

Manufacturers often must choose between outsourcing and producing internally. This choice is complex and influenced by a variety of factors, including the costs and capabilities of the potential suppliers. In addition, if the manufacturer outsources, he must design the sourcing process. We study the manufacturer's outsourcing decision, with a focus on the impact of the sourcing process on that decision. We consider a setting in which the manufacturer has imperfect information regarding the suppliers' costs and capabilities, and we assume that the manufacturer uses a two‐stage sourcing process. The first stage is the qualification stage, in which the manufacturer seeks to reduce the uncertainty regarding the suppliers' capabilities. The second stage is the supplier selection stage, in which the manufacturer selects among the qualified suppliers on the basis of price. We first characterize the optimal design of the two‐stage process, and then consider the outsourcing decision. We demonstrate several trade‐offs. Vertical integration enables the manufacturer to reduce uncertainty and extract all of the profits of production. However, outsourcing enables the manufacturer to take advantage of the (potentially) lower costs and higher capabilities of the suppliers, particularly if competition between suppliers can be encouraged. We find that the manufacturer is more likely to vertically integrate when the warranty cost and the cost of exerting effort during qualification are large, and when there is significant uncertainty regarding the suppliers' capabilities. The manufacturer is more likely to outsource when the suppliers' costs (capabilities) are low (high), and when the number of suppliers is large.     

Entry Deterrence of Capacitated Competition Using Price and Non‐Price Strategies

We analyze the role of pricing and branding in an incumbent firm's decision when facing competition from an entrant firm with limited capacity. We do so by studying two price competition models (Stackelberg and Nash), where we consider the incumbent's entry‐deterrence pricing strategy based on a potential entrant's capacity size. In an extension, we also study a branding model, where the incumbent firm, in addition to pricing, can also invest in influencing market preference for its product. With these models, we study conditions under which the incumbent firm may block the entrant (i.e., prevent entry without any market actions), deter the entrant (i.e., stop entry with suitable market actions) or accommodate the entrant (i.e., allow entry and compete), and how the entrant will allocate its limited capacity across its own and the new market, if entry occurs. We also study the timing difference between the two different dynamics of the price competition models and find that the incumbent's first‐mover advantage benefits both the incumbent and the entrant. Interestingly, the entrant firm's profits are not monotonically increasing in its capacity even when it is costless to build capacity. In the branding model, we show that in some cases, the incumbent may even increase its price and successfully deter entry by investing in consumer's preference for its product. Finally, we incorporate demand uncertainty into our model and show that the incumbent benefits from demand uncertainty while the entrant may be worse off depending on the magnitude of demand uncertainty and its capacity.     

Multiobjective investment planning under uncertainty

In this paper we consider the relevance of various planning methods and decision criteria to multiobjective investment planning under uncertainty. Assuming that a natural reaction to uncertainty is to operate so as to leave open as many good options as possible (as opposed to maximizing subjective expected utility) we argue that the planning process should concentrate on analyzing the effects of the initial decision, and that for this exercise the classical methods of mixed integer programming are inappropriate. We demonstrate how the technique of dynamic programming can be extended to take account of multiple objectives and use dynamic programming as a framework in which we analyze the robustness of an initial decision in the face of various types of uncertainty. In so doing we also analyze the risks involved in both the planning and decision making functions.     

A Framework for Understanding Uncertainty in Seismic Risk Assessment

A better understanding of the uncertainty that exists in models used for seismic risk assessment is critical to improving risk-based decisions pertaining to earthquake safety. Current models estimating the probability of collapse of a building do not consider comprehensively the nature and impact of uncertainty. This article presents a model framework to enhance seismic risk assessment and thus gives decisionmakers a fuller understanding of the nature and limitations of the estimates. This can help ensure that risks are not over- or underestimated and the value of acquiring accurate data is appreciated fully. The methodology presented provides a novel treatment of uncertainties in input variables, their propagation through the model, and their effect on the results. The study presents ranges of possible annual collapse probabilities for different case studies on buildings in different parts of the world, exposed to different levels of seismicity, and with different vulnerabilities. A global sensitivity analysis was conducted to determine the significance of uncertain variables. Two key outcomes are (1) that the uncertainty in ground-motion conversion equations has the largest effect on the uncertainty in the calculation of annual collapse probability; and (2) the vulnerability of a building appears to have an effect on the range of annual collapse probabilities produced, i.e., the level of uncertainty in the estimate of annual collapse probability, with less vulnerable buildings having a smaller uncertainty.     

Stochastic lot sizing problem with controllable processing times

In this study, we consider the stochastic capacitated lot sizing problem with controllable processing times where processing times can be reduced in return for extra compression cost. We assume that the compression cost function is a convex function as it may reflect increasing marginal costs of larger reductions and may be more appropriate when the resource life, energy consumption or carbon emission are taken into consideration. We consider this problem under static uncertainty strategy and α service level constraints. We first introduce a nonlinear mixed integer programming formulation of the problem, and use the recent advances in second order cone programming to strengthen it and then solve by a commercial solver. Our computational experiments show that taking the processing times as constant may lead to more costly production plans, and the value of controllable processing times becomes more evident for a stochastic environment with a limited capacity. Moreover, we observe that controllable processing times increase the solution flexibility and provide a better solution in most of the problem instances, although the largest improvements are obtained when setup costs are high and the system has medium sized capacities.     

Quantifying Water Pathogen Risk in an Epidemiological Framework

Traditionally, microbial risk assessors have used point estimates to evaluate the probability that an individual will become infected. We developed a quantitative approach that shifts the risk characterization perspective from point estimate to distributional estimate, and from individual to population. To this end, we first designed and implemented a dynamic model that tracks traditional epidemiological variables such as the number of susceptible, infected, diseased, and immune, and environmental variables such as pathogen density. Second, we used a simulation methodology that explicitly acknowledges the uncertainty and variability associated with the data. Specifically, the approach consists of assigning probability distributions to each parameter, sampling from these distributions for Monte Carlo simulations, and using a binary classification to assess the output of each simulation. A case study is presented that explores the uncertainties in assessing the risk of giardiasis when swimming in a recreational impoundment using reclaimed water. Using literature-based information to assign parameters ranges, our analysis demonstrated that the parameter describing the shedding of pathogens by infected swimmers was the factor that contributed most to the uncertainty in risk. The importance of other parameters was dependent on reducing the a priori range of this shedding parameter. By constraining the shedding parameter to its lower subrange, treatment efficiency was the parameter most important in predicting whether a simulation resulted in prevalences above or below non outbreak levels. Whereas parameters associated with human exposure were important when the shedding parameter was constrained to a higher subrange. This Monte Carlo simulation technique identified conditions in which outbreaks and/or nonoutbreaks are likely and identified the parameters that most contributed to the uncertainty associated with a risk prediction.     

Naturally Occurring Preferences and Exogenous Laboratory Experiments: A Case Study of Risk Aversion

Does individual behavior in a laboratory setting provide a reliable indicator of behavior in a naturally occurring setting? We consider this general methodological question in the context of eliciting risk attitudes. The controls that are typically employed in laboratory settings, such as the use of abstract lotteries, could lead subjects to employ behavioral rules that differ from the ones they employ in the field. Because it is field behavior that we are interested in understanding, those controls might be a confound in themselves if they result in differences in behavior. We find that the use of artificial monetary prizes provides a reliable measure of risk attitudes when the natural counterpart outcome has minimal uncertainty, but that it can provide an unreliable measure when the natural counterpart outcome has background risk. Behavior tended to be moderately risk averse when artificial monetary prizes were used or when there was minimal uncertainty in the natural nonmonetary outcome, but subjects drawn from the same population were much more risk averse when their attitudes were elicited using the natural nonmonetary outcome that had some background risk. These results are consistent with conventional expected utility theory for the effects of background risk on attitudes to risk.