Info-gap Research Articles

Reliability assessment of explosive material based on penalty tests: An info-gap approach

A method is developed for experimental assessment of the reliability of a system with a stringent safety requirement: explosive material. The focus is on the analysis and management of both statistical variability of measurements and non-probabilistic uncertainty in probability distributions (distributional uncertainty). Info-gap theory is used to model the distributional uncertainty in the probability distribution function of the threshold for actuation of the explosive material. The quantitative analysis and the qualitative judgements which accompany the certification of safety are studied. A proposition is proven asserting that the info-gap robustness function, for the class of problems examined, is independent of the experimental design over virtually all of its range.

Detection capacity, information gaps and the design of surveillance programs for invasive forest pests

Integrated pest risk maps and their underlying assessments provide broad guidance for establishing surveillance programs for invasive species, but they rarely account for knowledge gaps regarding the pest of interest or how these can be reduced. In this study we demonstrate how the somewhat competing notions of robustness to uncertainty and potential knowledge gains could be used in prioritizing large-scale surveillance activities. We illustrate this approach with the example of an invasive pest recently detected in North America, Sirex noctilio Fabricius. First, we formulate existing knowledge about the pest into a stochastic model and use the model to estimate the expected utility of surveillance efforts across the landscape. The expected utility accounts for the distribution, abundance and susceptibility of the host resource as well as the value of timely S. noctilio detections. Next, we make use of the info-gap decision theory framework to explore two alternative pest surveillance strategies. The first strategy aims for timely, certain detections and attempts to maximize the robustness to uncertainty about S. noctilio behavior; the second strategy aims to maximize the potential knowledge gain about the pest via unanticipated (i.e., opportune) detections. The results include a set of spatial outputs for each strategy that can be used independently to prioritize surveillance efforts. However, we demonstrate an alternative approach in which these outputs are combined via the Pareto ranking technique into a single priority map that outlines the survey regions with the best trade-offs between both surveillance strategies.

Info-gap decision theory and its potential applications in the clinic.

Personalized medicine seeks to match innate characteristics of patients with potential interventions in order to secure the most favorable outcome while mitigating risk. Personalized medicine does not supplant the decisions made by health care professionals in conjunction with patients. In fact, ideally, the application of personalized medicine greatly augments the quality of that interaction by adding an objective measure of disease and response to the physician's professional judgment. In that context, the practitioner faces a disparity between what is known and what needs to be known in order to realize the desired goal of a favorable outcome of treatment or an effective avoidance of disease or complication. Info-gap theory can help manage this challenge. Physician and patient both wish to choose a course of action with confidence that the consequence will be satisfactory to the patient. However, these two attributes of a treatment - success and reliability - are different from each other and conflict with each other. Ambitious goals may be risky. The crux of the challenge is uncertainty: fragmentary data and imperfect understanding. Choices that exhaustively exploit uncertain knowledge may tend to fall short of the quality of outcome which is predicted by that knowledge, precisely because some of that knowledge is imprecise. On the other hand, better-than-anticipated outcomes are also possible when our knowledge is imperfect. Treatments must be selected not only according to their predicted outcomes, but also according to the immunity of those outcomes to errors in the knowledge underlying the predictions, and according to the opportunities inherent in the uncertainty. Info-gap decision theory [1] provides a tool for evaluating both the robustness against pernicious uncertainty as well as the opportuneness from propitious uncertainty. Info-gap theory is a methodology for decision under severe uncertainty which has been applied in many disciplines [101].

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.

Heterogeneous uncertainties in cholesterol management

Physicians use clinical guidelines to inform judgment about therapy. Clinical guidelines do not address three important uncertainties: (1) uncertain relevance of tested populations to the individual patient, (2) the patient’s uncertain preferences among possible outcomes, and (3) uncertain subjective and financial costs of intervention. Unreliable probabilistic information is available for some of these uncertainties; no probabilities are available for others. The uncertainties are in the values of parameters and in the shapes of functions. We explore the usefulness of info-gap decision theory in patient-physician decision making in managing cholesterol level using clinical guidelines. Info-gap models of uncertainty provide versatile tools for quantifying diverse uncertainties. Info-gap theory provides two decision functions for evaluating alternative therapies. The robustness function assesses the confidence—in light of uncertainties—in attaining acceptable outcomes. The opportuneness function assesses the potential for better-than-anticipated outcomes. Both functions assist in forming preferences among alternatives. Hypothetical case studies demonstrate that decisions using the guidelines and based on best estimates of the expected utility are sometimes, but not always, consistent with robustness and opportuneness analyses. The info-gap analysis provides guidance when judgment suggests that a deviation from the guidelines would be productive. Finally, analysis of uncertainty can help resolve ambiguous situations.

Info-gap theory and robust design of surveillance for invasive species: The case study of Barrow Island

Surveillance for invasive non-indigenous species (NIS) is an integral part of a quarantine system. Estimating the efficiency of a surveillance strategy relies on many uncertain parameters estimated by experts, such as the efficiency of its components in face of the specific NIS, the ability of the NIS to inhabit different environments, and so on. Due to the importance of detecting an invasive NIS within a critical period of time, it is crucial that these uncertainties be accounted for in the design of the surveillance system. We formulate a detection model that takes into account, in addition to structured sampling for incursive NIS, incidental detection by untrained workers. We use info-gap theory for satisficing (not minimizing) the probability of detection, while at the same time maximizing the robustness to uncertainty. We demonstrate the trade-off between robustness to uncertainty, and an increase in the required probability of detection. An empirical example based on the detection of Pheidole megacephala on Barrow Island demonstrates the use of info-gap analysis to select a surveillance strategy.

Do we know how to set decision thresholds for diabetes?

The diagnosis of diabetes, based on measured fasting plasma glucose level, depends on choosing a threshold level for which the probability of failing to detect disease (missed diagnosis), as well as the probability of falsely diagnosing disease (false alarm), are both small. The Bayesian risk provides a tool for aggregating and evaluating the risks of missed diagnosis and false alarm. However, the underlying probability distributions are uncertain, which makes the choice of the decision threshold difficult. We discuss an hypothesis for choosing the threshold that can robustly achieve acceptable risk. Our analysis is based on info-gap decision theory, which is a non-probabilistic methodology for modelling and managing uncertainty. Our hypothesis is that the non-probabilistic method of info-gap robust decision making is able to select decision thresholds according to their probability of success. This hypothesis is motivated by the relationship between info-gap robustness and the probability of success, which has been observed in other disciplines (biology and economics). If true, it provides a valuable clinical tool, enabling the clinician to make reliable diagnostic decisions in the absence of extensive probabilistic information. Specifically, the hypothesis asserts that the physician is able to choose a diagnostic threshold that maximizes the probability of acceptably small Bayesian risk, without requiring accurate knowledge of the underlying probability distributions. The actual value of the Bayesian risk remains uncertain.

Info-Gap Decision Theory for Assessing the Management of Catchments for Timber Production and Urban Water Supply

While previous studies have examined how forest management is influenced by the risk of fire, they rely on probabilistic estimates of the occurrence and impacts of fire. However, nonprobabilistic approaches are required for assessing the importance of fire risk when data are poor but risks are appreciable. We explore impacts of fire risk on forest management using as a case study a water catchment in the Australian Capital Territory (ACT) (southeastern Australia). In this forested area, urban water supply and timber yields from exotic plantations are potential joint but also competing land uses. Our analyses were stimulated by extensive wildfires in early 2003 that burned much of the existing exotic pine plantation estate in the water catchment and the resulting need to explore the relative economic benefits of revegetating the catchment with exotic plantations or native vegetation. The current mean fire interval in the ACT is approximately 40 years, making the establishment of a pine plantation economically marginal at a 4% discount rate. However, the relative impact on water yield of revegetation with native species and pines is very uncertain, as is the risk of fire under climate change. We use info-gap decision theory to account for these nonprobabilistic sources of uncertainty, demonstrating that the decision that is most robust to uncertainty is highly sensitive to the cost of native revegetation. If costs of native revegetation are sufficiently small, this option is more robust to uncertainty than revegetation with a commercial pine plantation.

Info‐Gap Robust‐Satisficing Model of Foraging Behavior: Do Foragers Optimize or Satisfice?

In this note we compare two mathematical models of foraging that reflect two competing theories of animal behavior: optimizing and robust satisficing. The optimal-foraging model is based on the marginal value theorem (MVT). The robust-satisficing model developed here is an application of info-gap decision theory. The info-gap robust-satisficing model relates to the same circumstances described by the MVT. We show how these two alternatives translate into specific predictions that at some points are quite disparate. We test these alternative predictions against available data collected in numerous field studies with a large number of species from diverse taxonomic groups. We show that a large majority of studies appear to support the robust-satisficing model and reject the optimal-foraging model.

A robust model-based test planning procedure

A wide variety of model-based optimal test design methodologies have been developed in the past decade using deterministic approaches. This means that the test planning is based on a single-nominal model and an optimal design is obtained for precisely this model. Needless to say, the deterministic approach can lead to an ineffective distribution of sensors and poorly defined excitation points due to the presence of epistemic modelling errors. In this article, a robust-satisficing design approach to test planning is proposed based on info-gap decision theory. This methodology provides a decision-making tool for better understanding the trade-off between an optimal test design with no robustness to modelling uncertainties and a sub-optimal design which satisfies a less demanding level of performance while remaining maximally robust with respect to a given horizon of info-gap model uncertainty. The proposed strategy is illustrated using an aerospace application under base excitation conditions.

Uncertainty, probability and information-gaps

Abstract This paper discusses two main ideas. First, we focus on info-gap uncertainty, as distinct from probability. Info-gap theory is especially suited for modelling and managing uncertainty in system models: we invest all our knowledge in formulating the best possible model; this leaves the modeller with very faulty and fragmentary information about the variation of reality around that optimal model. Second, we examine the interdependence between uncertainty modelling and decision-making. Good uncertainty modelling requires contact with the end-use, namely, with the decision-making application of the uncertainty model. The most important avenue of uncertainty-propagation is from initial data- and model-uncertainties into uncertainty in the decision-domain. Two questions arise. Is the decision robust to the initial uncertainties? Is the decision prone to opportune windfall success? We apply info-gap robustness and opportunity functions to the analysis of representation and propagation of uncertainty in several of the Sandia Challenge Problems.

半正定値計画法を用いた応力制約を有するトラスのロバスト性最大化

A robust truss optimization scheme, as well as an optimization algorithm, is presented based on the robustness function. Under the uncertainties of external forces modeled by using the info-gap decision theory, we formulate the maximization problem of the robustness function. A sequential semidefinite programming method is proposed which has the global convergent property. It is shown, in numerical examples, that optimum designs of various trusses can be found without any difficulty.

Review of Information-gap decision theory: Decisions under severe uncertainty by Yakov Ben-Haim

This book examines uncertainty from a nonprobabilistic point of view. The author is concerned with the development of info-gap models that seek to define the disparity between what is known and what could be known, with very little information about the structure of the uncertainty. Clustering of events is the central concept used in info-gap models of uncertainty rather than the frequency of recurrence, likelihood, plausibility, or possibility of events. The book is theoretical in nature with several theorems but contains many examples from structural mechanics, project management, and various other disciplines. The author puts forth the notion that probability models do not capture all facets of the phenomena associated with risk taking. However, he also recognizes that some information is modeled well probabilistically. Therefore, hybrid probabilistic/info-gap decision algorithms are also explored in the book. Chapter 1 gives an overview of the various parts of the book, while Chapter 2 gives milestones of the development of uncertainty from numbers to statistics, quantum mechanics and nonlinear dynamics. The author describes the different forms of uncertainty, including linguistic, and uncertainty caused by sparse information. The chapter contains contrasts between info-gap uncertainty models, and distribution-based models including probabilistic and fuzzy models with physical examples. The mathematical definition of an info-gap model of uncertainty is given, and various forms of info-gap models are presented. Chapter 3 introduces the robustness function, which is defined as the immunity to failure and the opportunity function, which expresses the immunity to windfall gain; these are the basic decision functions in info-gap decision theory. The author explains that when robustness is large, the decision is unaffected by large errors in the information; on the other hand, the opportunity function is the lowest level of uncertainty that can enable ~but not guarantee! a large windfall reward. The components of info-gap decision theory are defined, and examples such as vibrations of a cantilever beam under uncertain loads are used to implement infogap decision models. Structural reliability is treated in the context of the robustness function in terms of a threshold robustness based on acceptable levels of risk.