The Experts below are selected from a list of 9075 Experts worldwide ranked by ideXlab platform
Philip A Dawid - One of the best experts on this subject based on the ideXlab platform.
-
game Theory maximum entropy minimum discrepancy and robust Bayesian Decision Theory
arXiv: Statistics Theory, 2004Co-Authors: Peter Grunwald, Philip A DawidAbstract:We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium Theory of zero-sum games between Decision Maker and Nature, these two problems are shown to be dual to each other, the solution to each providing that to the other. Although Tops\oe described this connection for the Shannon entropy over 20 years ago, it does not appear to be widely known even in that important special case. We here generalize this Theory to apply to arbitrary Decision problems and loss functions. We indicate how an appropriate generalized definition of entropy can be associated with such a problem, and we show that, subject to certain regularity conditions, the above-mentioned duality continues to apply in this extended context. This simultaneously provides a possible rationale for maximizing entropy and a tool for finding robust Bayes acts. We also describe the essential identity between the problem of maximizing entropy and that of minimizing a related discrepancy or divergence between distributions. This leads to an extension, to arbitrary discrepancies, of a well-known minimax theorem for the case of Kullback-Leibler divergence (the ``redundancy-capacity theorem'' of information Theory). For the important case of families of distributions having certain mean values specified, we develop simple sufficient conditions and methods for identifying the desired solutions.
-
game Theory maximum entropy minimum discrepancy and robust Bayesian Decision Theory
Annals of Statistics, 2004Co-Authors: Peter Grunwald, Philip A DawidAbstract:We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium Theory of zero-sum games between Decision Maker and Nature, these two problems are shown to be dual to each other, the solution to each providing that to the other. Although Topsoe described this connection for the Shannon entropy over 20 years ago, it does not appear to be widely known even in that important special case. We here generalize this Theory to apply to arbitrary Decision problems and loss functions. We indicate how an appropriate generalized definition of entropy can be associated with such a problem, and we show that, subject to certain regularity conditions, the above-mentioned duality continues to apply in this extended context. This simultaneously provides a possible rationale for maximizing entropy and a tool for finding robust Bayes acts. We also describe the essential identity between the problem of maximizing entropy and that of minimizing a related discrepancy or divergence between distributions. This leads to an extension, to arbitrary discrepancies, of a well-known minimax theorem for the case of Kullback-Leibler divergence (the redundancy-capacity theorem of information Theory). For the important case of families of distributions having certain mean values specified, we develop simple sufficient conditions and methods for identifying the desired solutions. We use this Theory to introduce a new concept of generalized exponential family linked to the specific Decision problem under consideration, and we demonstrate that this shares many of the properties of standard exponential families. Finally, we show that the existence of an equilibrium in our game can be rephrased in terms of a Pythagorean property of the related divergence, thus generalizing previously announced results for Kullback-Leibler and Bregman divergences.
Peter Grunwald - One of the best experts on this subject based on the ideXlab platform.
-
game Theory maximum entropy minimum discrepancy and robust Bayesian Decision Theory
arXiv: Statistics Theory, 2004Co-Authors: Peter Grunwald, Philip A DawidAbstract:We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium Theory of zero-sum games between Decision Maker and Nature, these two problems are shown to be dual to each other, the solution to each providing that to the other. Although Tops\oe described this connection for the Shannon entropy over 20 years ago, it does not appear to be widely known even in that important special case. We here generalize this Theory to apply to arbitrary Decision problems and loss functions. We indicate how an appropriate generalized definition of entropy can be associated with such a problem, and we show that, subject to certain regularity conditions, the above-mentioned duality continues to apply in this extended context. This simultaneously provides a possible rationale for maximizing entropy and a tool for finding robust Bayes acts. We also describe the essential identity between the problem of maximizing entropy and that of minimizing a related discrepancy or divergence between distributions. This leads to an extension, to arbitrary discrepancies, of a well-known minimax theorem for the case of Kullback-Leibler divergence (the ``redundancy-capacity theorem'' of information Theory). For the important case of families of distributions having certain mean values specified, we develop simple sufficient conditions and methods for identifying the desired solutions.
-
game Theory maximum entropy minimum discrepancy and robust Bayesian Decision Theory
Annals of Statistics, 2004Co-Authors: Peter Grunwald, Philip A DawidAbstract:We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium Theory of zero-sum games between Decision Maker and Nature, these two problems are shown to be dual to each other, the solution to each providing that to the other. Although Topsoe described this connection for the Shannon entropy over 20 years ago, it does not appear to be widely known even in that important special case. We here generalize this Theory to apply to arbitrary Decision problems and loss functions. We indicate how an appropriate generalized definition of entropy can be associated with such a problem, and we show that, subject to certain regularity conditions, the above-mentioned duality continues to apply in this extended context. This simultaneously provides a possible rationale for maximizing entropy and a tool for finding robust Bayes acts. We also describe the essential identity between the problem of maximizing entropy and that of minimizing a related discrepancy or divergence between distributions. This leads to an extension, to arbitrary discrepancies, of a well-known minimax theorem for the case of Kullback-Leibler divergence (the redundancy-capacity theorem of information Theory). For the important case of families of distributions having certain mean values specified, we develop simple sufficient conditions and methods for identifying the desired solutions. We use this Theory to introduce a new concept of generalized exponential family linked to the specific Decision problem under consideration, and we demonstrate that this shares many of the properties of standard exponential families. Finally, we show that the existence of an equilibrium in our game can be rephrased in terms of a Pythagorean property of the related divergence, thus generalizing previously announced results for Kullback-Leibler and Bregman divergences.
Katz Charles - One of the best experts on this subject based on the ideXlab platform.
-
Bayesian Decision Theory for tree-based adaptive screening tests with an application to youth delinquency
2021Co-Authors: Krantsevich Chelsea, Hahn P. Richard, Yi Zheng, Katz CharlesAbstract:Crime prevention strategies based on early intervention depend on accurate risk assessment instruments for identifying high risk youth. It is important in this context that the instruments be convenient to administer, which means, in particular, that they should also be reasonably brief; adaptive screening tests are useful for this purpose. Adaptive tests constructed using classification and regression trees are becoming a popular alternative to traditional Item Response Theory (IRT) approaches for adaptive testing. However, tree-based adaptive tests lack a principled criterion for terminating the test. This paper develops a Bayesian Decision Theory framework for measuring the trade-off between brevity and accuracy, when considering tree-based adaptive screening tests of different lengths. We also present a novel method for designing tree-based adaptive tests, motivated by this framework. The framework and associated adaptive test method are demonstrated through an application to youth delinquency risk assessment in Honduras; it is shown that an adaptive test requiring a subject to answer fewer than 10 questions can identify high risk youth nearly as accurately as an unabridged survey containing 173 items.Comment: 20 pages, 11 figure
-
Bayesian Decision Theory for tree-based adaptive screening tests with an application to youth delinquency
2021Co-Authors: Krantsevich Chelsea, Hahn P. Richard, Yi Zheng, Katz CharlesAbstract:Crime prevention strategies based on early intervention depend on accurate risk assessment instruments for identifying high risk youth. It is important in this context that the instruments be convenient to administer, which means, in particular, that they must be reasonably brief; adaptive screening tests are useful for this purpose. Although item response Theory (IRT) bears a long and rich history in producing reliable adaptive tests, adaptive tests constructed using classification and regression trees are becoming a popular alternative to the traditional IRT approach for item selection. On the upside, unlike IRT, tree-based questionnaires require no real-time parameter estimation during administration. On the downside, while item response Theory provides robust criteria for terminating the exam, the stopping criterion for a tree-based adaptive test (the maximum tree depth) is unclear. We present a Bayesian Decision Theory approach for characterizing the trade-offs of administering tree-based questionnaires of different lengths. This formalism involves specifying 1) a utility function measuring the goodness of the assessment; 2) a target population over which this utility should be maximized; 3) an action space comprised of different-length assessments, populated via a tree-fitting algorithm. Using this framework, we provide uncertainty estimates for the trade-offs of shortening the exam, allowing practitioners to determine an optimal exam length in a principled way. The method is demonstrated through an application to youth delinquency risk assessment in Honduras.Comment: 20 pages, 11 figure
Nathan Favero - One of the best experts on this subject based on the ideXlab platform.
-
performance gaps and managerial Decisions a Bayesian Decision Theory of managerial action
Journal of Public Administration Research and Theory, 2015Co-Authors: Kenneth J Meier, Nathan Favero, Ling ZhuAbstract:An extensive literature finds that managerial Decisions matter for the performance of public organizations, yet little attention has been devoted to why managers make the Decisions that they do. This article builds a Theory of public management Decision making based on the simple assumption that managers are concerned with performance and the performance gaps of their organization. Using a logic borrowed from bounded rationality and Bayesian Decision Theory, we theorize a set of prior expectations. Whether the organization meets these expectations or fails to do so is then used to specify a series of precise hypotheses about when managers make a variety of Decisions including when to seek additional information, take risks, decentralize the organization, determine goals, or select a managerial strategy as well as other managerial actions. The logic of the Theory can easily be extended to Decisions about selecting goals or managerial strategy. We then extend the basic Theory by considering multiple goals, hierarchy, and alternative theoretical approaches.
John Dalsgaard Sørensen - One of the best experts on this subject based on the ideXlab platform.
-
framework for risk based planning of operation and maintenance for offshore wind turbines
Wind Energy, 2009Co-Authors: John Dalsgaard SørensenAbstract:For offshore wind turbines, costs to operation and maintenance (OM) are substantial. This paper describes a risk-based life cycle approach for optimal planning of OM. The approach is based on pre-posterior Bayesian Decision Theory, and can be used both to overall, initial planning of OM, and to sequential optimal Decision making on planning of OM taking into account new information. Deterioration mechanisms such as fatigue, corrosion, wear and erosion are associated with significant uncertainty. Observations of the degree of damage can increase the reliability of predictions, especially in connection with condition-based maintenance. The approach can be used for gearboxes, generators, fatigue cracks, corrosion, etc. This paper also describes how probabilistic indicators can be used to quantify indirect information about the damage state for critical components, e.g. gearboxes. Copyright © 2009 John Wiley & Sons, Ltd.
