What you can do with Coordinated Samples

Sample coordination, where similar instances have similar samples, was proposed by statisticians four decades ago as a way to maximize overlap in repeated surveys. Coordinated sampling had been since used for summarizing massive data sets. The usefulness of a sampling scheme hinges on the scope and accuracy within which queries posed over the original data can be answered from the sample. We aim here to gain a fundamental understanding of the limits and potential of coordination. Our main result is a precise characterization, in terms of simple properties of the estimated function, of queries for which estimators with desirable properties exist. We consider unbiasedness, nonnegativity, finite variance, and bounded estimates. Since generally a single estimator can not be optimal (minimize variance simultaneously) for all data, we propose {\em variance competitiveness}, which means that the expectation of the square on any data is not too far from the minimum one possible for the data. Surprisingly perhaps, we show how to construct, for any function for which an unbiased nonnegative estimator exists, a variance competitive estimator.Comment: 4 figures, 21 pages, Extended Abstract appeared in RANDOM 201

Robust Bayesian Inference for Set-Identified Models

This paper reconciles the asymptotic disagreement between Bayesian and frequentist inference in set‐identified models by adopting a multiple‐prior (robust) Bayesian approach. We propose new tools for Bayesian inference in set‐identified models and show that they have a well‐defined posterior interpretation in finite samples and are asymptotically valid from the frequentist perspective. The main idea is to construct a prior class that removes the source of the disagreement: the need to specify an unrevisable prior for the structural parameter given the reduced‐form parameter. The corresponding class of posteriors can be summarized by reporting the ‘posterior lower and upper probabilities’ of a given event and/or the ‘set of posterior means’ and the associated ‘robust credible region’. We show that the set of posterior means is a consistent estimator of the true identified set and the robust credible region has the correct frequentist asymptotic coverage for the true identified set if it is convex. Otherwise, the method provides posterior inference about the convex hull of the identified set. For impulse‐response analysis in set‐identified Structural Vector Autoregressions, the new tools can be used to overcome or quantify the sensitivity of standard Bayesian inference to the choice of an unrevisable prior

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Multivariate risk measures : a constructive approach based on selections

Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are set-valued. Furthermore, it is reasonable to include the exchange rules in the argument of the risk and so consider risk measures of set-valued portfolios. This situation includes the classical Kabanov's transaction costs model, where the set-valued portfolio is given by the sum of a random vector and an exchange cone, but also a number of further cases of additional liquidity constraints. The definition of the selection risk measure is based on calling a set-valued portfolio acceptable if it possesses a selection with all individually acceptable marginals. The obtained risk measure is coherent (or convex), law invariant and has values being upper convex closed sets. We describe the dual representation of the selection risk measure and suggest efficient ways of approximating it from below and from above. In case of Kabanov's exchange cone model, it is shown how the selection risk measure relates to the set-valued risk measures considered by Kulikov (2008), Hamel and Heyde (2010), and Hamel et al. (2013)Supported by the Spanish Ministry of Science and Innovation Grants No. MTM20II—22993 and ECO20ll-25706. Supported by the Chair of Excellence Programme of the Universidad Carlos III de Madrid and Banco Santander and the Swiss National Foundation Grant No. 200021-13752

Report of the Working Group on `W Mass and QCD' (Phenomenology Workshop on LEP2 Physics, Oxford, April 1997)

The W Mass and QCD Working Group discussed a wide variety of topics relating to present and future measurements of M(W) at LEP2, including QCD backgrounds to W+W- production. Particular attention was focused on experimental issues concerning the direct reconstruction and threshold mass measurements, and on theoretical and experimental issues concerning the four jet final state. This report summarises the main conclusions.Comment: 43 pages LaTeX and 15 encapsulated postscript figures. Uses epsfig and ioplppt macros. Full Proceedings to be published in Journal of Physics

Asymptotically Optimal Algorithms for Budgeted Multiple Play Bandits

We study a generalization of the multi-armed bandit problem with multiple plays where there is a cost associated with pulling each arm and the agent has a budget at each time that dictates how much she can expect to spend. We derive an asymptotic regret lower bound for any uniformly efficient algorithm in our setting. We then study a variant of Thompson sampling for Bernoulli rewards and a variant of KL-UCB for both single-parameter exponential families and bounded, finitely supported rewards. We show these algorithms are asymptotically optimal, both in rateand leading problem-dependent constants, including in the thick margin setting where multiple arms fall on the decision boundary

Communications Research

Contains reports on seven research projects