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Copula models are becoming increasingly popular in engineering and financial applications. They provide a flexible way of constructing joint distributions with arbitrary one-dimensional margins and a wide variety of dependence structures. This paper studies different types of conditionalization of copula-based models. We conditionalize these models in the usual way on point values but also propose a different type of conditionalization on a new margin. This new type of conditionalization is motivated by experience with a model built for application in modeling risk in civil aviation. Changing one margin in a copula model is very easy; however, it is not equivalent to conditionalizing on a new margin. For this purpose, the technique presented by Holland and Wang [Holland PW, Wang YJ (1987) Dependence function for continuous bivariate densities. Commun. Statist. Theory Methods 16(3):867-876], called marginal replacement, is used. The main result of this paper allows a simplified way of conditionalizing on more than one univariate margin in a normal copula model. [ABSTRACT FROM AUTHOR]

Several relevant problems in reliability can be looked at as problems of risk management and of decisions in the face of uncertainty. However, in this frame, the so-called burn-in problem can be seen as a problem of risk taking par excellence. In this paper, we in particular point out some aspects concerning interactions between the probabilistic model for lifetimes and considerations of an economic kind. As one of the features of our work, we hinge on some unexplored connections between ageing properties of a one-dimensional survival function ... and risk-aversion-type properties of the function u(t) = bG(t), b > 0, when the latter is seen as a utility function. [ABSTRACT FROM AUTHOR]

Decision analysis problems have traditionally been solved using either decision trees or influence diagrams. Although decision trees are better at handling asymmetry, prevalent in many reliability and risk analysis problems, influence diagrams can solve larger real-world problems by exploiting conditional independence. Decision circuits are graphical representations that combine the computational benefits of both graphical models. They are syntactic representations, i.e., they depict the summation, multiplication, and maximization operations required to solve a decision analysis problem. Previous work on decision circuits has focused on compiling them automatically from influence diagrams and describing the ways in which they can be used for efficient solution and sensitivity analysis. In this paper, we show how a decision circuit can be formulated directly, with or without the preprocessing of numbers that are assessed from the decision maker. By constructing two decision circuits for a nuclear reactor example, one using probabilities in inferred form and the other using probabilities in assessed form, we show how decision circuits generalize decision trees. The notion of coalescence is also made more explicit because computations for decision analysis can be saved and then reused in several ways. Because of their generality, decision circuits provide the analyst with a great deal of flexibility in problem formulation. [ABSTRACT FROM AUTHOR]

Adversarial risk analysis is an active and important area of decision analytic research. Both single-actor decision analysis and multiple-actor game theory have been applied to this problem, with game theoretic methods being particularly popular. Although game theory models do explicitly capture strategic interactions between attackers and defenders, two of the key assumptions--decision making based on subjective expected utility maximization and common knowledge of rationality--are known to be descriptively inaccurate in some situations. This paper addresses these shortcomings by proposing, formulating, and illustrating the application of robust optimization methodologies to a level-k game theory model for adversarial risk analysis. Level-k game theory provides a practical method for modeling bounded rationality. Robust optimization provides an alternative way to model the actions of conservative players facing "deep" uncertainties about their environment--uncertainties that are possible to bound but that are difficult or impossible to represent using probability distributions. Our approach thus combines level-k and robust optimization insights to provide a computationally tractable model of boundedly rational players who are faced with significant and difficult to quantify uncertainties. [ABSTRACT FROM AUTHOR]

In standard models of Bayesian learning, agents reduce their uncertainty about an event's true probability because their consistent estimator concentrates almost surely around this probability's true value as the number of observations becomes large. This paper takes the empirically observed violations of Savage's (Savage, L. J. 1954. The Foundations of Statistics. John Wiley & Sons, New York) sure thing principle seriously and asks whether Bayesian learners with ambiguity attitudes will reduce their ambiguity when sample information becomes large. To address this question, I develop closed-form models of Bayesian learning in which beliefs are described as Choquet estimators with respect to neoadditive capacities (Chateauneuf, A., J. Eichberger, S. Grant. 2007. Choice under uncertainty with the best and worst in mind: Neo-additive capacities. J. Econom. Theory 137(1) 538-567). Under the optimistic, the pessimistic, and the full Bayesian update rules, a Bayesian learner's ambiguity will increase rather than decrease to the effect that these agents will express ambiguity attitudes regardless of whether they have access to large sample information or not. Although consistent Bayesian learning occurs under the Sarin and Wakker (Sarin, R., P. P. Wakker. 1998b. Revealed likelihood and Knightian uncertainty. J. Risk Uncertainty 16(3) 223-250) update rule, this result comes with the descriptive drawback that it does not apply to agents who still express ambiguity attitudes after one round of updating. [ABSTRACT FROM AUTHOR]

Decision analysis has traditionally been applied to choices under uncertainty involving a single decision maker. Game theory has been applied to solving games of strategic interaction between two or more players. Building upon recent work of van Binsbergen and Marx (van Binsbergen, J. H., L. M. Marx. 2007. Exploring relations between decision analysis and game theory. Decision Anal. 4(1) 32-40), this paper defines a modified decision-theoretic approach to solving games of strategic interaction between two players. Using this method, the choices of the two players are modeled with separate decision trees comprised entirely of chance nodes. Optimal policies are reflected in the probabilities in the decision trees of each player. In many cases, the Nash equilibrium strategy for each player can be obtained by rolling back the opponent's decision tree. Results are demonstrated for the multistage signaling game, which is difficult to model using decision nodes to represent strategies, as in the approach of van Binsbergen and Marx. [ABSTRACT FROM AUTHOR]

This paper presents a decision tree model for evaluating countermeasures to reduce vulnerabilities to terrorism in commercial truck crossings at United States southwestern land ports of entry. The model includes critical events in four phases of cargo movement: cargo transfer in Mexico, Mexican customs, U.S. customs, and the inland phase. Improvements in transportation security, inspections at Mexican ports, and at U.S. ports, are comparatively evaluated using parameterized variables. Costs and benefits of such improvements are analyzed to counter a radiological dispersion device (also known as a "dirty bomb") attack. The results suggest that security decisions depend primarily on the probability of attack and parameters that influence the overall cost of false alarms. Extensive exploratory analysis reveals that improving security at Mexican ports is not recommended, mainly due to the cost of false alarms. However, a high percentage and a high cost of false alarms may justify new radiation portal monitors at U.S. ports even when improvements in the capability to detect dangerous cargo are insignificant. Better transportation security is not recommended if the probability of attack is less than 0.15. When the probability of attack exceeds 0.15 and false-alarm related costs are high, the model recommends enhancing transportation security. In addition, the parameters modeling economic consequences of an attack in a populated area, the probability of discovering weapons after smuggling into the United States, the probability of detonation, as well as the probability of detection at U.S. ports of entry, have significant impact on the countermeasure decision. [ABSTRACT FROM AUTHOR]

For this final issue of the year, our first two articles are on assessment of probabilities. First, Joel B. Predd, Daniel N. Osherson, Sanjeev R. Kulkarni, and H. Vincent Poor present a method for "Aggregating Probabilistic Forecasts from Incoherent and Abstaining Experts." In our second article, Ali E. Abbas, David V. Budescu, Hsiu-Ting Yu, and Ryan Haggerty present the results of their experiment in "A Comparison of Two Probability Encoding Methods: Fixed Probability vs. Fixed Variable Values." Next, a new method for searching among a huge set of alternatives using preference information is presented in "An Interactive Search Method Based on User Preferences," by Asim Roy, Patrick Mackin, Jyrki Wallenius, James Corner, Mark Keith, Gregory Schymik, and Hina Arora. In our final article, Niyazi Onur Bakir describes how to use decision analysis to compare antiterrorism measures in "A Decision Tree Model for Evaluating Countermeasures to Secure Cargo at United States Southwestern Ports of Entry." A call for papers on auctions for a special issue in memory of Michael Rothkopf is announced in this issue. The annual thank you to reviewers ends the issue. [ABSTRACT FROM AUTHOR]

Decision makers often rely on expert opinion when making forecasts under uncertainty. In doing so, they confront two methodological challenges: the elicitation problem, which requires them to extract meaningful information from experts; and the aggregation problem, which requires them to combine expert opinion by resolving disagreements. Linear averaging is a justifiably popular method for addressing aggregation, but its robust simplicity makes two requirements on elicitation. First, each expert must offer probabilistically coherent forecasts; second, each expert must respond to all our queries. In practice, human judges (even experts) may be incoherent, and may prefer to assess only the subset of events about which they are comfortable offering art opinion. In this paper, a new methodology is developed for combining expert assessment of chance. The method retains the conceptual and computational simplicity of linear averaging, but generalizes the standard approach by relaxing the requirements on expert elicitation. The method also enjoys provable performance guarantees, and in experiments with real-world forecasting data is shown to offer both computational efficiency and competitive forecasting gains as compared to rival aggregation methods. This paper is relevant to the practice of decision analysis, for it enables an elicitation methodology in which judges have freedom to choose the events they assess. [ABSTRACT FROM AUTHOR]

This paper develops a theory of risk attitudes that can be applied in a broad array of settings, including those in which the decision maker (DM) abides by a preference model other than the expected utility model and in which decisions are being made over multiattribute alternatives. The theory is based on (i) a set of plausible axioms in which the DM's preferences over consequences and lotteries are defined separately and (ii) the premise that a risk neutral DM is indifferent between a lottery and the average (in terms of preference) of the outcomes obtained from infinite repetition of the lottery. We show that, under these assumptions, a risk neutral DM seeks to maximize the expectation of classic cardinal utility (i.e., measurable value). This means, in particular, that the DM's risk attitude in expected utility theory is related to the transformation function between the classic cardinal utility function and the von Neumann-Morgenstern utility function. The results also suggest that the applicability of the conventional definitions of risk attitudes may be limited to settings in which the DM's classic cardinal utility function is linear and that a more generalized treatment of risk attitudes is required for settings in which this is not the case. [ABSTRACT FROM AUTHOR]

With ever-increasing terror threats, governments and security officials would benefit from a better understanding of what motivates terrorists to cause social unrest. A recent research trend is on gaining greater knowledge about the values of malicious agents to help manage the risk of terrorism. As a result, there seems to be the potential to use decision analysis as a means to model what may drive malicious agents to commit harmful actions. So far, research on this topic has assumed static preferences of such agents. In this paper, we present a framework that may be used to infer how terrorists' priorities may change over time and their impact on their choice of a harmful action. We suggest modeling state-dependent priorities of a terrorist group via a multicriteria model that incorporates state-dependent priorities to account for preference change caused by exogenous triggers and representing the environment as a system dynamics model. We describe how terrorists' visceral factors may affect the prioritization of objectives and show how such an analysis may support risk management in this context. [ABSTRACT FROM AUTHOR]

This paper presents a general method for interactively searching for objects (alternatives) in a large collection the contents of which are unknown to the user and where the objects are defined by a large number of discrete-valued attributes. Briefly, the method presents an object and asks the user to indicate his or her preference for the object. The method allows preference indications in two basic modes: (1) by assignment of objects to predefined preference categories such as high, medium, and low preference or (2) by direct preference comparison of objects such as "object A preferred to object B." From these preference statements, the method learns about the user's preferences and constructs an approximation to a value or preference function of the user (additive or multiplicative) at each iteration. It then uses this approximate preference function to rerank the objects in the collection and retrieve the top-ranked ones to present to the user at the next iteration. The process terminates when the user is satisfied with the list of top-ranked objects. This method can also be used to solve general multiattribute discrete alternative problems, where the alternatives are known with certainty and described by a set of discrete-valued attributes. Test results are reported and application possibilities are discussed. [ABSTRACT FROM AUTHOR]

A buyer seeks to purchase an asset from a seller who has a finite time T in which to sell his asset. Either the buyer's offer is permanent and remains available until time T , or it is an exploding offer and remains in effect only at the instant it is made. Our goal is to determine when an exploding offer maximizes the buyer's probability of purchasing the asset (at the given offer price). We embed our analysis in a standard continuous time finite horizon search model with recall in which only one buyer is strategic and considers making an exploding offer. Our analysis and examples reveal that the strategic buyer's choice of offer duration is complex: almost anything can occur. We obtain an explicit characterization of the optimal choice when the offer distribution is uniform. [ABSTRACT FROM AUTHOR]

We model a dynamic purchase context in which a consumer is uncertain about the product's valuation. The consumer has two purchase opportunities for the product: forward purchase in Period 1 or spot purchase in Period 2. Two forms of regret are considered: buyer's regret over the money paid in excess of his valuation of the product when buying forward and hesitater's regret for the lost opportunity of an increased surplus when not buying forward. We illustrate how regrets affect the purchase decision: a consumer is more likely to buy forward when more averse to hesitater's regret but more likely to delay the decision when more averse to buyer's regret. We also consider alternative consumer types to characterize how regret affects their spot purchase decisions as well as what triggers the regret. We show that type inconsistency--that is, a consumer's incorrect anticipation of his future type--induces an inferior Period 1 purchase decision and thereby reduces the consumer's expected surplus. [ABSTRACT FROM AUTHOR]

This paper presents a decision analysis method for evaluating computer intrusion detection systems. The method integrates and extends receiver operating characteristic (ROC) and cost analysis methods to provide an expected cost metric. We demonstrate that both the ROC analysis and cost analysis methods are incomplete. Furthermore, we demonstrate how a decision tree can combine and extend the ROC and cost analysis methods to provide an expected cost metric that reflects the intrusion detection system's ROC curve, costs, and assessments of the hostility of the environment as summarized by the prior probability of intrusion. We further demonstrate how this method can be used to decide the optimal operating point on an intrusion detector's ROC curve, choose the best intrusion detection system, compare the value of one intrusion detection system with another's, determine the value of an intrusion detector over no detector, and determine how to adjust the operation of an intrusion detector to respond to changes in its environment. General results are given and the method is illustrated in several numerical examples that involve both hypothetical and real intrusion detection systems. We demonstrate that, contrary to common advice, the value of an intrusion detection system depends not only on its ROC curve, but also on various costs (such as those associated with making incorrect decisions about detection) and the hostility of the operating environment. Conclusions are drawn about the design and evaluation of intrusion detection systems and the role for decision analysis in that design and evaluation. [ABSTRACT FROM AUTHOR]

Good analysis alone may not achieve the goals of decision analysis (DA) engagements. Good communication of the results of that analysis can help stakeholders understand, accept, and implement the recommended course of action. Practitioners can use decision-analytic principles when considering the decision of how to communicate results themselves. From this perspective, we consider a range of questions to ask in preparing for communication with the client and other stakeholders. We review standard communication practices in DA engagements. The standard practice can be improved by drawing on insights from other areas of management practice. Decision analysis has both technical and organizational features, and we discuss ways to deal with the conceptual and expressive challenges this presents. This pragmatic tutorial provides a starting point for decision analysts to develop both technical communication skills and organizational communication skills. [ABSTRACT FROM AUTHOR]

We show how adversarial risk analysis may cope with a current important security issue in relation with piracy off the Somali coasts. Specifically, we describe how to support the owner of a ship in managing risks from piracy in that area. We illustrate how a sequential defend--attack--defend model can be used to formulate this decision problem and solve it for the ship owner. Our formulation models the pirates' behavior through the analysis of how they could solve their decision problem. [ABSTRACT FROM AUTHOR]

Although a wide variety of sensitivity analysis methods for additive value models appear in the literature, the most commonly used and easily understood is one-way sensitivity analysis. We address concerns from practice with this traditional method and build the mathematical foundation for a new and robust one-way sensitivity analysis approach that enables the decision maker(s) to gain a greater ownership of the model. A traditional one-way sensitivity analysis varies one attribute weight while keeping all others proportionally constant; although useful, it also has limitations, particularly in group decision making. Our proposed methodology, customizable one-way sensitivity analysis (COSA), retains the simplicity of the traditional method but extends it to a more powerful form. COSA allows the decision maker(s) to tailor the sensitivity analysis to the desired decision context by assigning weight coefficients of elasticity to the attribute weights. These parameters let the decision maker choose how the adjusted weight change is distributed throughout the model. Furthermore, we provide a detailed discussion about performing sensitivity analysis on complex hierarchies with more than one tier and include an applied example to demonstrate COSAAlthough a wide variety of sensitivity analysis methods for additive value models appear in the literature, the most commonly used and easily understood is one-way sensitivity analysis. We address concerns from practice with this traditional method and build the mathematical foundation for a new and robust one-way sensitivity analysis approach that enables the decision maker(s) to gain a greater ownership of the model. A traditional one-way sensitivity analysis varies one attribute weight while keeping all others proportionally constant; although useful, it also has limitations, particularly in group decision making. Our proposed methodology, customizable one-way sensitivity analysis (COSA), retains the simplicity of the traditional method but extends it to a more powerful form. COSA allows the decision maker(s) to tailor the sensitivity analysis to the desired decision context by assigning weight coefficients of elasticity to the attribute weights. These parameters let the decision maker choose how the adjusted weight change is distributed throughout the model. Furthermore, we provide a detailed discussion about performing sensitivity analysis on complex hierarchies with more than one tier and include an applied example to demonstrate COSAAlthough a wide variety of sensitivity analysis methods for additive value models appear in the literature, the most commonly used and easily understood is one-way sensitivity analysis. We address concerns from practice with this traditional method and build the mathematical foundation for a new and robust one-way sensitivity analysis approach that enables the decision maker(s) to gain a greater ownership of the model. A traditional one-way sensitivity analysis varies one attribute weight while keeping all others proportionally constant; although useful, it also has limitations, particularly in group decision making. Our proposed methodology, customizable one-way sensitivity analysis (COSA), retains the simplicity of the traditional method but extends it to a more powerful form. COSA allows the decision maker(s) to tailor the sensitivity analysis to the desired decision context by assigning weight coefficients of elasticity to the attribute weights. These parameters let the decision maker choose how the adjusted weight change is distributed throughout the model. Furthermore, we provide a detailed discussion about performing sensitivity analysis on complex hierarchies with more than one tier and include an applied example to demonstrate COSA's usefulness. Overall, a consistent standard for the one-way sensitivity analysis of additive value models is provided for the decision analysis community. s usefulness. Overall, a consistent standard for the one-way sensitivity analysis of additive value models is provided for the decision analysis community. s usefulness. Overall, a consistent standard for the one-way sensitivity analysis of additive value models is provided for the decision analysis community. [ABSTRACT FROM AUTHOR]

When scoring rules were first widely used, they were developed as a way to measure the accuracy of probability forecasts ex post. Ex ante, proper scoring rules encourage honestly reported and sharper probabilities, both of which increase the forecaster's expected score. Most applications utilize standard off-the shelf scoring rules. In the spirit of decision analysis, we develop proper scoring rules that are tailored to specific decision-making problems and to the utility functions of particular decision makers. We show how these rules, which are intended for situations where a decision maker consults an expert to assess a probability, not only encourage honest reporting, but also reward sharpness in a way that aligns the interests of the expert and the decision maker. We also illustrate the generation of tailored scoring rules in numerical form, which is useful when analytical expressions for the tailored rules cannot be obtained or are too complex to be helpful in practice. Finally, we show how these numerical scoring rules can be presented to the expert in graphical or tabular form and suggest that this could be desirable even for standard scoring rules. [ABSTRACT FROM AUTHOR]

The equivalence of two elicitation methods (sequences and matching) has been assumed when empirically testing the traditional discounting model even though the respective literature has revealed results that are dependent on the procedure used. Three common anomalies revealed (gain/loss asymmetry, short/long asymmetry, and the absolute magnitude effect) are investigated using the two different methods in a within-subjects experiment. In both procedures, it appears that the participants in this study evaluate monetary outcomes over time differently than the discounting model predicts. Patterns consistent with two of the anomalies (gain/loss and absolute magnitude effect) surface and interact in both elicitation techniques. Finally, a systematic inconsistency exists between the two methods. We observe significantly more consistency between the two elicitation techniques when the outcome is a gain in the relatively far future than when it is a future loss. This may be due to the participants' inability to display a preference for spreading losses, which they revealed in the sequences task, in the matching task. [ABSTRACT FROM AUTHOR]

In multiattribute portfolio optimization, a decision maker must evaluate a number of projects on multiple dimensions and then select the set of projects that optimizes the portfolio's overall value. In this note, we discuss the importance of establishing an appropriate baseline score for not doing a project in multiattribute portfolio analysis. We believe that practitioners often implicitly assume that not doing a project results in the worst possible score on all attributes. We argue that this assumption is often inappropriate and may lead to incorrect recommendations. [ABSTRACT FROM AUTHOR]

We present the results of an experiment comparing two popular methods for encoding probability distributions of continuous variables in decision analysis: eliciting values of a variable, X, through comparisons with a fixed probability wheel and eliciting the percentiles of the cumulative distribution, F(X), through comparisons with fixed values of the variable. We show slight but consistent superiority for the fixed variable method along several dimensions such as monotonicity, accuracy, and precision of the estimated fractiles. The fixed variable elicitation method was also slightly faster and preferred by most participants. We discuss the reasons for its superiority and conclude with several recommendations for the practice of probability assessment. [ABSTRACT FROM AUTHOR]