22,725 research outputs found

    Elicitation of ambiguous beliefs with mixing bets

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    I consider the elicitation of ambiguous beliefs about an event and show how to identify the interval of relevant probabilities (representing ambiguity perception) for several classes of ambiguity averse preferences. The agent reveals her preference for mixing binarized bets on the uncertain event and its complement under varying betting odds. Under ambiguity aversion, mixing is informative about the interval of beliefs. In particular, the mechanism allows to distinguish ambiguous beliefs from point beliefs, and identifies the belief interval for maxmin preferences. For ambiguity averse smooth second order and variational preferences, the mechanism reveals inner bounds for the belief interval, which are sharp under additional assumptions. In an experimental study, participants perceive almost as much ambiguity for natural events (generated by the stock exchange and by a prisoners dilemma game) as for the Ellsberg Urn, indicating that ambiguity may play a role in real-world decision making

    Bayes linear kinematics in the analysis of failure rates and failure time distributions

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    Collections of related Poisson or binomial counts arise, for example, from a number of different failures in similar machines or neighbouring time periods. A conventional Bayesian analysis requires a rather indirect prior specification and intensive numerical methods for posterior evaluations. An alternative approach using Bayes linear kinematics in which simple conjugate specifications for individual counts are linked through a Bayes linear belief structure is presented. Intensive numerical methods are not required. The use of transformations of the binomial and Poisson parameters is proposed. The approach is illustrated in two examples, one involving a Poisson count of failures, the other involving a binomial count in an analysis of failure times

    Bayesian multitask inverse reinforcement learning

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    We generalise the problem of inverse reinforcement learning to multiple tasks, from multiple demonstrations. Each one may represent one expert trying to solve a different task, or as different experts trying to solve the same task. Our main contribution is to formalise the problem as statistical preference elicitation, via a number of structured priors, whose form captures our biases about the relatedness of different tasks or expert policies. In doing so, we introduce a prior on policy optimality, which is more natural to specify. We show that our framework allows us not only to learn to efficiently from multiple experts but to also effectively differentiate between the goals of each. Possible applications include analysing the intrinsic motivations of subjects in behavioural experiments and learning from multiple teachers.Comment: Corrected version. 13 pages, 8 figure

    Imperfect Recall and Time Inconsistencies: An experimental test of the absentminded driver "paradox"

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    Absentmindedness is a special case of imperfect recall which according to Piccione and Rubinstein (1997a) leads to time inconsistencies. Aumann, Hart and Perry (1997a) question their argument and show how dynamic inconsistencies can be resolved. The present paper explores this issue from a descriptive point of view by examining the behavior of absentminded individuals in a laboratory environment. Absentmindedness is manipulated in two ways. In one treatment, it is induced by cognitively overloading participants. In the other, it is imposed by randomly matching decisions with decision nodes in the information set. The results provide evidence for time inconsistencies in all treatments. We introduce a behavioral principal, which best explains the data.imperfect recall, absentmindedness, dynamic inconsistency, experiment

    Expert Elicitation for Reliable System Design

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    This paper reviews the role of expert judgement to support reliability assessments within the systems engineering design process. Generic design processes are described to give the context and a discussion is given about the nature of the reliability assessments required in the different systems engineering phases. It is argued that, as far as meeting reliability requirements is concerned, the whole design process is more akin to a statistical control process than to a straightforward statistical problem of assessing an unknown distribution. This leads to features of the expert judgement problem in the design context which are substantially different from those seen, for example, in risk assessment. In particular, the role of experts in problem structuring and in developing failure mitigation options is much more prominent, and there is a need to take into account the reliability potential for future mitigation measures downstream in the system life cycle. An overview is given of the stakeholders typically involved in large scale systems engineering design projects, and this is used to argue the need for methods that expose potential judgemental biases in order to generate analyses that can be said to provide rational consensus about uncertainties. Finally, a number of key points are developed with the aim of moving toward a framework that provides a holistic method for tracking reliability assessment through the design process.Comment: This paper commented in: [arXiv:0708.0285], [arXiv:0708.0287], [arXiv:0708.0288]. Rejoinder in [arXiv:0708.0293]. Published at http://dx.doi.org/10.1214/088342306000000510 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Joint estimation of multiple related biological networks

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    Graphical models are widely used to make inferences concerning interplay in multivariate systems. In many applications, data are collected from multiple related but nonidentical units whose underlying networks may differ but are likely to share features. Here we present a hierarchical Bayesian formulation for joint estimation of multiple networks in this nonidentically distributed setting. The approach is general: given a suitable class of graphical models, it uses an exchangeability assumption on networks to provide a corresponding joint formulation. Motivated by emerging experimental designs in molecular biology, we focus on time-course data with interventions, using dynamic Bayesian networks as the graphical models. We introduce a computationally efficient, deterministic algorithm for exact joint inference in this setting. We provide an upper bound on the gains that joint estimation offers relative to separate estimation for each network and empirical results that support and extend the theory, including an extensive simulation study and an application to proteomic data from human cancer cell lines. Finally, we describe approximations that are still more computationally efficient than the exact algorithm and that also demonstrate good empirical performance.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS761 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org
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