Why Risk Analysis is Difficult,and Some Thoughts on How to Proceed

Risk analysis is challenged in three ways by uncertainty. Our understanding of the world and its uncertainties is evolving; indeterminism is an inherent part of the open universe in which we live; and learning from experience involves untestable assumptions. We discuss several concepts of robustness as tools for responding to these epistemological challenges. The use of models is justified, even though they are known to err. A concept of robustness is illustrated in choosing between a conventional technology and an innovative, promising, but more uncertain technology. We explain that nonprobabilistic robust decisions are sometimes good probabilistic bets. Info‐gap and worst‐case concepts of robustness are compared. Finally, we examine the exploitation of favorable but uncertain opportunities and its relation to robust decision making.     

Reasoned Decision Making Without Math? Adaptability and Robustness in Response to Surprise

Many real‐world planning and decision problems are far too uncertain, too variable, and too complicated to support realistic mathematical models. Nonetheless, we explain the usefulness, in these situations, of qualitative insights from mathematical decision theory. We demonstrate the integration of info‐gap robustness in decision problems in which surprise and ignorance are predominant and where personal and collective psychological factors are critical. We present practical guidelines for employing adaptable‐choice strategies as a proxy for robustness against uncertainty. These guidelines include being prepared for more surprises than we intuitively expect, retaining sufficiently many options to avoid premature closure and conflicts among preferences, and prioritizing outcomes that are steerable, whose consequences are observable, and that do not entail sunk costs, resource depletion, or high transition costs. We illustrate these concepts and guidelines with the example of the medical management of the 2003 SARS outbreak in Vietnam.     

Multiple Temptations

We use a preference‐over‐menus framework to model a decision maker who is affected by multiple temptations. Our two main axioms on preference—exclusion and inclusion—identify when the agent would want to restrict his choice set and when he would want to expand his choice set. An agent who is tempted would want to restrict his choice set by excluding the normatively worst alternative of that choice set. Simultaneously, he would want to expand his choice set by including a normatively superior alternative. Our representation identifies the agent's normative preference and temptations, and suggests the agent is uncertain which of these temptations will affect him. We provide examples to illustrate how our model improves on those of Gul and Pesendorfer (2001) and Dekel, Lipman, and Rustichini (2009).     

Fooled by Local Robustness

One would have expected the considerable public debate created by Nassim Taleb’s two best selling books on uncertainty, Fooled by Randomness and The Black Swan, to inspire greater caution to the fundamental difficulties posed by severe uncertainty. Yet, methodologies exhibiting an incautious approach to uncertainty have been proposed recently in a range of publications. So, the objective of this short note is to call attention to a prime example of an incautious approach to severe uncertainty that is manifested in the proposition to use the concept radius of stability as a measure of robustness against severe uncertainty. The central proposition of this approach, which is exemplified in info‐gap decision theory, is this: use a simple radius of stability model to analyze and manage a severe uncertainty that is characterized by a vast uncertainty space, a poor point estimate, and a likelihood‐free quantification of uncertainty. This short discussion serves then as a reminder that the generic radius of stability model is a model of local robustness. It is, therefore, utterly unsuitable for the treatment of severe uncertainty when the latter is characterized by a poor estimate of the parameter of interest, a vast uncertainty space, and a likelihood‐free quantification of uncertainty.     

Stochastic Choice and Revealed Perturbed Utility

Perturbed utility functions—the sum of expected utility and a nonlinear perturbation function—provide a simple and tractable way to model various sorts of stochastic choice. We provide two easily understood conditions each of which characterizes this representation: One condition generalizes the acyclicity condition used in revealed preference theory, and the other generalizes Luce's IIA condition. We relate the discrimination or selectivity of choice rules to properties of their associated perturbations, both across different agents and across decision problems. We also show that these representations correspond to a form of ambiguity‐averse preferences for an agent who is uncertain about her true utility.     

Robust Climate Policies Under Uncertainty: A Comparison of Robust Decision Making and Info‐Gap Methods

This study compares two widely used approaches for robustness analysis of decision problems: the info‐gap method originally developed by Ben‐Haim and the robust decision making (RDM) approach originally developed by Lempert, Popper, and Bankes. The study uses each approach to evaluate alternative paths for climate‐altering greenhouse gas emissions given the potential for nonlinear threshold responses in the climate system, significant uncertainty about such a threshold response and a variety of other key parameters, as well as the ability to learn about any threshold responses over time. Info‐gap and RDM share many similarities. Both represent uncertainty as sets of multiple plausible futures, and both seek to identify robust strategies whose performance is insensitive to uncertainties. Yet they also exhibit important differences, as they arrange their analyses in different orders, treat losses and gains in different ways, and take different approaches to imprecise probabilistic information. The study finds that the two approaches reach similar but not identical policy recommendations and that their differing attributes raise important questions about their appropriate roles in decision support applications. The comparison not only improves understanding of these specific methods, it also suggests some broader insights into robustness approaches and a framework for comparing them.     

Reconciling Uncertain Costs and Benefits in Bayes Nets for Invasive Species Management

Bayes nets are used increasingly to characterize environmental systems and formalize probabilistic reasoning to support decision making. These networks treat probabilities as exact quantities. Sensitivity analysis can be used to evaluate the importance of assumptions and parameter estimates. Here, we outline an application of info‐gap theory to Bayes nets that evaluates the sensitivity of decisions to possibly large errors in the underlying probability estimates and utilities. We apply it to an example of management and eradication of Red Imported Fire Ants in Southern Queensland, Australia and show how changes in management decisions can be justified when uncertainty is considered.     

Benchmark Dose Analysis via Nonparametric Regression Modeling

Estimation of benchmark doses (BMDs) in quantitative risk assessment traditionally is based upon parametric dose‐response modeling. It is a well‐known concern, however, that if the chosen parametric model is uncertain and/or misspecified, inaccurate and possibly unsafe low‐dose inferences can result. We describe a nonparametric approach for estimating BMDs with quantal‐response data based on an isotonic regression method, and also study use of corresponding, nonparametric, bootstrap‐based confidence limits for the BMD. We explore the confidence limits’ small‐sample properties via a simulation study, and illustrate the calculations with an example from cancer risk assessment. It is seen that this nonparametric approach can provide a useful alternative for BMD estimation when faced with the problem of parametric model uncertainty.     

Wavelet‐Based Testing for Serial Correlation of Unknown Form in Panel Models

Wavelet analysis is a new mathematical method developed as a unified field of science over the last decade or so. As a spatially adaptive analytic tool, wavelets are useful for capturing serial correlation where the spectrum has peaks or kinks, as can arise from persistent dependence, seasonality, and other kinds of periodicity. This paper proposes a new class of generally applicable wavelet‐based tests for serial correlation of unknown form in the estimated residuals of a panel regression model, where error components can be one‐way or two‐way, individual and time effects can be fixed or random, and regressors may contain lagged dependent variables or deterministic/stochastic trending variables. Our tests are applicable to unbalanced heterogenous panel data. They have a convenient null limit N(0,1) distribution. No formulation of an alternative model is required, and our tests are consistent against serial correlation of unknown form even in the presence of substantial inhomogeneity in serial correlation across individuals. This is in contrast to existing serial correlation tests for panel models, which ignore inhomogeneity in serial correlation across individuals by assuming a common alternative, and thus have no power against the alternatives where the average of serial correlations among individuals is close to zero. We propose and justify a data‐driven method to choose the smoothing parameter—the finest scale in wavelet spectral estimation, making the tests completely operational in practice. The data‐driven finest scale automatically converges to zero under the null hypothesis of no serial correlation and diverges to infinity as the sample size increases under the alternative, ensuring the consistency of our tests. Simulation shows that our tests perform well in small and finite samples relative to some existing tests.     

Ignorance Is Not Probability

The distinction between ignorance about a parameter and knowing only a probability distribution for that parameter is of fundamental importance in risk assessment. Brief dialogs between a hypothetical decisionmaker and a risk assessor illustrate this point, showing that the distinction has real consequences. These dialogs are followed by a short exposition that places risk analysis in a decision‐theoretic framework, describes the important elements of that framework, and uses these to shed light on Terje Aven's criticism of nonprobabilistic purely “objective” methods. Suggestions are offered concerning a more effective approach to evaluating those methods.     

委托─代理理论中自然状态的不确定性对最优契约影响的研究

本文考虑了委托─代理理论中代理人和委托人对于不确定的自然状态可能会有不同的概率,另外还考虑了自然状态对代理人努力负效用的影响,对委托─代理模型进行了拓展研究,使原有模型成为一个特例。通过一个简化的委托─代理框架进行分析,结果表明,代理人对自然状态的概率与代理人可能付出的努力水平有正相关关系,而且代理人和委托人对自然状态的概率对最优契约有不可忽视的影响。     

Health Care Supply Chain Design: Toward Linking the Development and Delivery of Care Globally*

This article is motivated by the gap between the growing demand and available supply of high‐quality, cost‐effective, and timely health care, a problem faced not only by developing and underdeveloped countries but also by developed countries. The significance of this problem is heightened when the economy is in recession. In an attempt to address the problem, in this article, first, we conceptualize care as a bundle of goods, services, and experiences—including diet and exercise, drugs, devices, invasive procedures, new biologics, travel and lodging, and payment and reimbursement. We then adopt a macro, end‐to‐end, supply chain–centric view of the health care sector to link the development of care with the delivery of care. This macro, supply chain–centric view sheds light on the interdependencies between key industries from the upstream to the downstream of the health care supply chain. We propose a framework, the 3A‐framework, that is founded on three constructs—affordability, access, and awareness—to inform the design of supply chain for the health care sector. We present an illustrative example of the framework toward designing the supply chain for implantable device–based care for cardiovascular diseases in developing countries. Specifically, the framework provides a lens for identifying an integrated system of continuous improvement and innovation initiatives relevant to bridging the gap between the demand and supply for high‐quality, cost‐effective, and timely care. Finally, we delineate directions of future research that are anchored in and follow from the developments documented in the article.     

Power Enhancement in High‐Dimensional Cross‐Sectional Tests

We propose a novel technique to boost the power of testing a high‐dimensional vector H : θ = 0 against sparse alternatives where the null hypothesis is violated by only a few components. Existing tests based on quadratic forms such as the Wald statistic often suffer from low powers due to the accumulation of errors in estimating high‐dimensional parameters. More powerful tests for sparse alternatives such as thresholding and extreme value tests, on the other hand, require either stringent conditions or bootstrap to derive the null distribution and often suffer from size distortions due to the slow convergence. Based on a screening technique, we introduce a “power enhancement component,” which is zero under the null hypothesis with high probability, but diverges quickly under sparse alternatives. The proposed test statistic combines the power enhancement component with an asymptotically pivotal statistic, and strengthens the power under sparse alternatives. The null distribution does not require stringent regularity conditions, and is completely determined by that of the pivotal statistic. The proposed methods are then applied to testing the factor pricing models and validating the cross‐sectional independence in panel data models.     

Unobservable Investment and the Hold‐Up Problem

We study a two‐person bargaining problem in which the buyer may invest and increase his valuation of the object before bargaining. We show that if all offers are made by the seller and the time between offers is small, then the buyer invests efficiently and the seller extracts all of the surplus. Hence, bargaining with frequently repeated offers remedies the hold‐up problem even when the agent who makes the relation‐specific investment has no bargaining power and contracting is not possible. We consider alternative formulations with uncertain gains from trade or two‐sided investment.     

Sequential Search and Selection Problem Under Uncertainty

This paper formulates and discusses a series of sequential decision problems of the following common structure: A decision alternative of multiple attributes‐that is, a job, an employee, or an investment alternative‐is to be selected within a certain fixed length of time. An unknown number of alternatives are presented sequentially, either deterministically or in a random manner. The decision maker can rank all the alternatives from best to worst without ties, and the decision to accept or reject an alternative is based solely on the relative ranks of those alternatives evaluated so far. The nonparametric sequential decision problem is first studied for a model involving a discrete time period and then generalized in terms of continuous time. Also considered is a variant of this problem involving a Bayesian estimation of (1) the uncertain probability of having an alternative at a given stage in the discrete‐time model and (2) the arrival rate of alternatives in the continuous‐time model. The optimal selection strategy that maximizes the probability of selecting the absolute best alternative is illustrated with the job search problem and the single‐machine job assignment problem.     

UNCERTAIN DEMAND,CONSUMER LOSS AVERSION,AND FLAT‐RATE TARIFFS

We consider a model of firm pricing and consumer choice, where consumers are loss averse and uncertain about their future demand. Possibly, consumers in our model prefer a flat rate to a measured tariff, even though this choice does not minimize their expected billing amount—a behavior in line with ample empirical evidence. We solve for the profit‐maximizing two‐part tariff, which is a flat rate if (a) marginal costs are not too high, (b) loss aversion is intense, and (c) there are strong variations in demand. Moreover, we analyze the optimal nonlinear tariff. This tariff has a large flat part when a flat rate is optimal among the class of two‐part tariffs.     

The Retail Planning Problem Under Demand Uncertainty

We consider the retail planning problem in which the retailer chooses suppliers and determines the production, distribution, and inventory planning for products with uncertain demand to minimize total expected costs. This problem is often faced by large retail chains that carry private‐label products. We formulate this problem as a convex‐mixed integer program and show that it is strongly NP‐hard. We determine a lower bound by applying a Lagrangian relaxation and show that this bound outperforms the standard convex programming relaxation while being computationally efficient. We also establish a worst‐case error bound for the Lagrangian relaxation. We then develop heuristics to generate feasible solutions. Our computational results indicate that our convex programming heuristic yields feasible solutions that are close to optimal with an average suboptimality gap at 3.4%. We also develop managerial insights for practitioners who choose suppliers and make production, distribution, and inventory decisions in the supply chain.     

Robustness of Risk Maps and Survey Networks to Knowledge Gaps About a New Invasive Pest

In pest risk assessment it is frequently necessary to make management decisions regarding emerging threats under severe uncertainty. Although risk maps provide useful decision support for invasive alien species, they rarely address knowledge gaps associated with the underlying risk model or how they may change the risk estimates. Failure to recognize uncertainty leads to risk‐ignorant decisions and miscalculation of expected impacts as well as the costs required to minimize these impacts. Here we use the information gap concept to evaluate the robustness of risk maps to uncertainties in key assumptions about an invading organism. We generate risk maps with a spatial model of invasion that simulates potential entries of an invasive pest via international marine shipments, their spread through a landscape, and establishment on a susceptible host. In particular, we focus on the question of how much uncertainty in risk model assumptions can be tolerated before the risk map loses its value. We outline this approach with an example of a forest pest recently detected in North America, Sirex noctilio Fabricius. The results provide a spatial representation of the robustness of predictions of S. noctilio invasion risk to uncertainty and show major geographic hotspots where the consideration of uncertainty in model parameters may change management decisions about a new invasive pest. We then illustrate how the dependency between the extent of uncertainties and the degree of robustness of a risk map can be used to select a surveillance network design that is most robust to knowledge gaps about the pest.