Info-gap Models Of Uncertainty Research Articles

Robustness, fidelity and prediction-looseness of models

Assessment of the credibility of a mathematical or numerical model of a complex system must combine three components: (i) the fidelity of the model to test data, e.g. as quantified by a mean-squared error; (ii) the robustness, of model fidelity, to lack of understanding of the underlying processes; and (iii) the prediction-looseness of the model. ‘Prediction-looseness’ is the range of predictions of models that are equivalent in terms of fidelity. The main result of this paper asserts that fidelity, robustness and prediction-looseness are mutually antagonistic. A change in the model that enhances one of these attributes will cause deterioration of another. In particular, increasing the fidelity to test data will decrease the robustness to imperfect understanding of the process. Likewise, increasing the robustness will increase the predictive looseness . The conclusion is that focusing only on fidelity-to-data is not a sound decision-making strategy for model building and validation. A better strategy is to explore the trade-offs between robustness-to-uncertainty, fidelity to data and tightness of predictions. Our analysis is based on info-gap models of uncertainty, which can be applied to cases of severe uncertainty and lack of knowledge.

Info-gap robust design with load and model uncertainties

This paper develops a new structural design concept which incorporates uncertainties in both the load and the structural model parameters. Info-gap models of uncertainty are used to represent uncertainty in the power spectral density of the load and in parameters of the vibration model of the structure. It is demonstrated that any design which optimizes functional performance will also minimize the robustness to uncertainty. Since uncertainties are prevalent in many applications, this paper argues that it is necessary to satisfy critical performance requirements (rather than to optimize performance), and to maximize the robustness to uncertainty. The design implications of this robust-satisficing approach are demonstrated with several heuristic structural design examples. It is shown that design preferences depend upon performance requirements: preferences between designs can be reversed when performance requirements change. Also, we show that the info-gap robustness function provides an attractive tool for adjudicating between conflicting objectives in multi-criteria design.

Home Bias in Financial Markets: Robust Satisficing with Info Gaps

Abstract: The observed patterns of equity portfolio allocation around the world are at odds with predictions from a capital asset pricing model (CAPM). What has come to be called the phenomenon is that investors tend to hold a disproportionately large share of their equity portfolio in home country stocks as compared with predictions of the CAPM. This paper provides an explanation of the home-bias phenomenon based on information-gap decision theory. The decision concept that is used here is that profit is satisficed and robustness to uncertainty is maximized rather than expected profit being maximized. Furthermore, uncertainty is modeled nonprobabilistically with info-gap models of uncertainty, which can be viewed as a possible quantification of Knightian uncertainty. JEL classification: D81, F30, G11, G15 Key words: equity home bias, Knightian uncertainty 1 Introduction The observed patterns of equity portfolio allocation around the world are at odds with predictions from the Capital Asset Price Models (CAPM) of Sharpe [16] and Lintner [13]. What has come to be called the 'home bias' phenomenon is that investors tend to hold a disproportionately large share of their equity portfolio in home country stocks, as compared with predictions of the CAPM. This paper provides an explanation of the home bias phenomenon based on information-gap decision theory. The decision concept which is used here is that profit is satisficed and robustness-to-uncertainty is maximized, rather than expected profit being maximized. Furthermore, uncertainty is modelled non-probabilistically with info-gap models of uncertainty. French and Poterba [6, 7] quantify the magnitude of the home bias for a number of countries and conclude that the size of the home bias is substantial, which led to the terms Home Bias Puzzle or French and Poterba Puzzle. For more details see Jeske [10]. In their calculations, French and Poterba assume that the investor maximizes the expected return decremented with a variance-based risk term. Let w = ([w.sub.h];[w.sub.f])' represent the vector of home and foreign investments, let [??] be the expected returns for home and foreign investments, and let [SIGMA] be the covariance matrix of returns. In the French and Poterba model, w is chosen to maximize U(w) = w'[??] - [lambda]/2 w'[SIGMA]w where [lambda] is chosen to weight the risk term. An extremum of U(w) occurs when [??] = [lambda][SIGMA]w. Let [w.sup.o] denote the observed portfolio weights for a particular country, so that the expected returns consistent with CAPM profit maximization would be [[??].sup.o] = [lambda][SIGMA][w.sup.o]. For the same country, let [w.sup.mc] denote the portfolio weights based on world market capitalization, without any home bias effect. That is, [w.sup.mc.sub.h] is the fraction of the world market capitalization ascribable to the country in question. For example, [w.sup.mc.sub.h] = 0.475 for the US. Without any home bias, one would expect that 47.5% of US investments would be in US assets. The vector of expected returns consistent with the CAPM, based on world market capitalization without home bias, is [[??].sup.mc] = [lambda][SIGMA][w.sup.mc]. French and Poterba observed, for a wide range of countries, that: [[??].sup.o.sub.h] > [[??].sup.mc.sub.h] and [[??].sup.o.sub.f] The returns vectors [[??].sup.o] and [[??].sup.mc] are not observed market values, but rather calculated values which are consistent with the CAPM decision model and observed portfolio weights. If the investor's behavior is rightly modelled by the CAPM theory, then [[??].sup.o] and [[??].sup.mc] can be interpreted as returns vectors which are anticipated or perceived by the investor. Relations (1) imply that investors perceive the domestic assets to perform better, and the foreign assets to perform worse, than the bias-free portfolio would indicate. …

不確定性を有する構造物のロバスト性の非確率的評価法

A new structural design concept is developed which incorporates uncertainties in both the load and the structural parameters. "Info-gap models of uncertainty" are used as non-probabilistic uncertainty models to represent uncertainties in the power soectral density of the dynamic disturbance and in parameters of the vibration model of the structure. Since uncertainties are prevalent in many situations, this paper discusses that it is necessary to satisfy critical performance requirements rather than optimizing performance, and to maximize the robustness to uncertainty. The design implications of this robust-satisficing approach are demonstrated with several structural design examples.

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.

Robustness of model-based fault diagnosis: Decisions with information-gap models of uncertainty

Fault diagnosis is analysed here as a decision between alternative hypotheses, based on uncertain evidence. W e consider severe lack of information, and perceive the uncertainty as an information gap between what is known, and what needs to be known for a perfect decision. This uncertainty is quantified with info-gap models of uncertainty, which require less information than probabilistic models. Previous work with convex set-models is extended to linear info-gap models which are not necessarily convex, as well as to more general info-gap models with arbitrary expansion properties. We define a decision algorithm based on info-gap models and prove three theorems, one establishing the connection with the earlier work on convex models, the other two showing that the algorithm is maximally robust for linear info-gap models as well as for general infogap models of uncertainty. An illustrative example is presented which shows how these results can be used for optimizing the design of a model-based fault diagnosis algorithm.

Design certification with information-gap uncertainty

This paper presents a concept for formulating structural design-codes which is based on information-gap models of uncertainty rather than on probabilistic concepts. Info-gap models quantify uncertainty as the size of the gap between what is known and what could be known. Info-gap models of uncertainty are particularly useful when data on the uncertainties are quite limited. In the proposed procedure a design is certified if the robustness to failure from uncertain fluctuations exceeds a code-specified threshold. Design is thus based on immunity to uncertainty rather than on probability of survival. The key conclusion is that design-certification can exploit data about uncertainties without introducing probabilistic models. This is important when information is scarce, since verification of probabilistic models can then be difficult. Second, when partial probabilistic information is available, it can be incorporated in a hybrid info-gap/probabilistic analysis. Third, the proposed design certification incorporates recognition of the dual nature of uncertainty: that it may be pernicious but may also entail propitious possibilities. Examples are presented which illustrate the design procedure. The incorporation of partial probabilistic information is also demonstrated. The antagonism between the pernicious and propitious potentials of ambient uncertainty is illustrated.